I'm curious about what you're husband's job is. Sounds like he's not a doctor?
UC is a really, really personal thing. The thing that gets in the way of it the most is fear, and one of the biggest sources of fear can be someone trained in medical birth.
As for what you need... First, know that if there's a situation where you, personally, would actually need oxygen, you need to transport. Even then, new standards of neonatal resuscitation say that room air (or the air from someone's lungs) is actually safer than oxygen. It's prudent for anyone, ANYONE who will be parenting to have first aid and CPR with infant CPR training. (I cannot tell you how many times I've had to rescue my youngest from choking). Likewise, if you're bleeding hard enough that home remedies and uterine massage aren't doing the trick, you need to transport. Administering pitocin yourself at home... if you need the pitocin, you probably need someone with more expertise evaluating the situation.
Midwives, at least, are trained to make that evaluation and handle things at home if they're not too serious. Planning a UC last time, my plan was for "as long as things are in the range of what I'm comfortable handling." When things got out of my comfort zone, it was time to ask for someone's help, and at that point, the midwife was good as a source of reassurance and kept me from transporting. What your "comfort zone" is is something only you can determine, and may well be different from mine.
Otherwise, it's pretty much what you might need at most homebirths. Absorbent stuff that you don't mind getting bloody or messy. Chux, or reusable pads, or a bunch of towels. A peri bottle for after (it just feels nicer than wiping). Something sterile to tie off or clamp the cord, whatever your preference is. Clean bedding (double-making the bed with a waterproof mattress cover between the layers is always good so that if you get messy in the bed, you're only a quick pull away from a clean set of sheets) and receiving blankets or soft towels for the baby.
For me, the point of planning a low-intervention birth (and I'm not planning a UC this time, but my midwife knows my "bent" and will not be surprised if she's in one room and I'm in another when the birth happens) is to give myself as much space as I possibly can to get into a biologically sound place to birth as simply as possible. Michel Odent describes the "Fetal Ejection reflex" and it requires that a mother be as undisturbed as possible. Disturbance can come from the inside, or from the outside, and can take the form of self-questioning (is this safe? Are things going right?) or a fearful partner, or a grabby midwife, or the hospital machine. Finding a space inside where you can listen to your body and get your head out of the way of it doing what it was made to do is key, and for some that means not even having anyone in the room, and for some that may mean NEEDING someone who is paying attention to the signs and signals and can keep reassuring that things are going well.
For me, once I hit a point where I knew I'd been pregnant as long as my body could stand to be (my bp was going up and I was starting to feel panicked about being pregnant another day), and was at a point where I was willing to consider castor oil to push things along, I was out of my comfort zone for not having someone there to check heart tones at key points. When yet another bout of contractions stopped, and I could feel my cervix really far open to not be having contractions, I needed another opinion on the matter. And what my midwife did was simply come down, listen to baby, check my cervix (my request, she would have been fine not), and confirm that yes, I was 6 cm and not having contractions, and that baby was doing okay. When I took some castor oil and landed in transition 10 minutes later, she listened and confirmed that baby was tolerating contractions well, which I needed to know since the contractions were stronger than they would have been without the intervention. When I could feel a long bag of waters protruding through a hard band of fully dilated, but not dilated enough cervix (the hard band was actually uterine muscle, not cervix per se, we realized later), every instinct in me said, "The bag of waters has to go for this baby to get born." So I ruptured it myself... and asked the midwife to check heart tones after I did so. And baby was fine, so I was able to let go any anxiety about that, and listen to my instincts. When my daughter was born, the midwife was standing nearby, but not touching me and mostly not talking to me, just being quiet and respectful of the space. And I was utterly, totally focused, felt everything I needed to do, did it.
When my baby was born looking odd and sounding wrong to me, the midwife was able to confirm that despite her odd noises, and odd features, her vitals were good and she was handling the transition well.
What we learned later was that my baby was born with a chromosome disorder, that her head was huge and had fused bones that could not mold. Every. Single. Instinct. was correct... both that things were off, and what needed to be done at every step of the way. But because what was happening was distinctly out of the normal range, the midwife was able to help keep me from being overwhelmed with fear about those things.
I said before labor, "It feels like my body wants to go into labor, but something has taped over the light switch." And it had... biologically I don't think she was capable of triggering labor, her metabolism is off, her hormone production is off, her basic processes of life do not function smoothly. She didn't even really open her eyes until what would have been 45 weeks gestation. So the smallest push had me into transition. I said during labor that the waters had to go for me to finish dilating...and since what we were dilating at that point was my uterus itself (I went to 12. TWELVE centimeters. Maybe 13. NOT ten) I was right.
The moment she was born, I said, "Something is wrong with her." And it was...it just didn't need instant intervention. We had a few blessed days of just being mother and baby, and not Dragon Mama with Broken Kid.
I said throughout pregnancy that my goal wasn't a particular kind of birth, not waterbirth, not UC, not even homebirth, but to make plans that would leave me room to listen to the quiet voice of intuition fully. My intuition rocks. I've saved my kid's life with my intuition. I've saved my own life and my mother's life with my intuition. And sometimes that intuition says, "We need help now." Sometimes it says, "We're okay."
I'm a DIY kinda gal. My family did everything for our wedding, from invites to catering to dyeing the danged fabric the dresses were made from. I've lanced infections in my children, I've made my own herbal medications, and even so, there are some times and places where my instinct says "This is out of my comfort zone."
The important thing is to find a way to create an environment where you are not afraid. I didn't, and don't, want to go to the hospital for birth. I refuse, despite being defined by the medical community as "high risk", to plan for a medicalized birth "just in case". But if we need that help, we'll get that help.
If your husband's skill set and HIS comfort zone are okay with some of the medical interventions, that's something you'll have to decide for yourself, but relying on that if he doesn't have the expertise to determine when they're necessary... the problem with interventions is that EVERY intervention carries some risk with it. Heck, not using interventions carries some risk. The art of it is knowing when intervention is helpful and when it will interfere.
IVs, for example. Why do women need IVs in labor? Well, for one, many hospitals don't let them eat or drink in labor, so women get dehydrated without. But at home, you can drink to thirst and eat to hunger, and your need for an IV is much less likely.
Why do babies need oxygen after birth? Well, in most cases, they don't. There are some times when a baby has a difficult transition, when they'll need help breathing, but that can be accomplished in most cases with puffs of air from the cheeks of a mother or midwife. At the hospital, more babies need resuscitation because more mothers are medicated in labor and more babies are born by cesarean, which doesn't stimulate the breathing processes the same way as vaginal births.
Why do mothers need pitocin after birth? Well, most don't, if they've been allowed to labor without medications or pitocin. But when you introduce external oxytocin in the bloodstream, it shuts down production in the brain, which can cause postpartum bleeding. These aren' the only reasons, but they're some of the biggest ones. Sometimes if labor has gone on a long time, the uterus is tired and needs some help. Why does labor go on a long time... it varies. Sometimes it just does. But sometimes the mother has been disturbed one way or another or things aren't lined up right, and the body has to work harder than it might otherwise to get the baby born.
What are some other causes of postpartum bleeding? Well, fiddling with the placenta is HUGE. Women who have been anesthetized (epidural) may require more help getting the placenta out. Cesarean section almost always causes more blood loss than a vaginal birth would. For me, I never let myself lie down until the placenta was out. In both cases, 5-10 minutes after baby was born, I stood up and the placenta just fell out. As a VBAC mom, you have some increased risk that the placenta won't come out easily, because of the uterine scar. You may have to listen closely to your instincts on that one... at what point you go in if it doesn't come out on its own. At home, you're not tied to a bed, you will NOT have been on pitocin (needing pitocin during labor is an absolute indication for needing hospital transport because pitocin carries risks with it that really need hospital backup to mitigate.) and if your'e sensible, no one will have been tugging on the thing.
The vast majority of things that go wrong in birth give warning signals that allow plenty of time to act, but only if you're willing to act. Most of the time things go well, especially in a healthy, well-nourished, unafraid mother who isn't being messed with. But there are no guarantees. There is no training in the world that will guarantee you a perfectly safe birth anywhere, period. Stuff happens. But you can plan for "as safe as we can make it", and that doesn't necessarily mean following anyone else's playbook.