Homeopathics are extremely dilute (so much so they don't contain any molecules of the original plant) they are an energetic medicine. The beneifit being that they are no side effects. If you use the wrong one, it simply won't work. But when it provides the energetic stimulus your body needs it can restore the body to a state of balance and nudge things in the right direction. For birth I always keep arnica on hand but would also personally have pulsatilla, cimicifuga (black cohosh) and caullophyllum (blue cohosh).
Tinctures are an alcohol extract of an herb. They are very potent medicine! The alcohol extracts out the active medicinal compounds in the herbs and creates a preparation that is fast acting and easy to administer. You can purchase "glycerites" which are glycerin based tinctures. This is fine for a few herbs, but not most. Many of the medicinal properties are not extracted into glycerin. There are a few companies that make their glycerites specifically in a way that does extract all of the medicine without any alcohol in the final product but unless you know their manufacturing process, it's best to stick with traditional tinctures. It is also importnat to remember that just because it is "natural" does not mean it is 100% safe. There is a time and a place to use the stronger acting tinctures, but it is best to have some herbal background to know what to administer when and in what dosage.
For birth, I would personally keep on hand:
*Motherwort (1 droperful under the tongue in between baby and placenta to help the placenta release and the uterus contract, or 1-2 dropperfuls in water for postpartum cramping)
*Angelica (1 dropperful under the tongue every 15 minutes as needed for retained placenta or clots)
*Shepherd's Purse in case of severe hemorrhage (1-2 dropperfuls under the tongue) but bear in mind that Shepherd's purse can cause very large clots to form resulting in concealed bleeding. You need to monitor fundal height carefully in the immediate postpartum if you've used Shepherd's Purse. Alternatively, you could use Yarrow or Lady's Mantle for postpartum bleeding/hemorrhage.
*Cramp Bark (2 dropperfuls in water for postpartum cramping).
*As an herbalist and midwife I do carry Black and Blue cohosh in my herbal birth kit but I very rarely use these. Personally, I don't think they are necessary for a UC as they are strong medicine, but they are excellent herbs to stimulate the uterus to contract. They can be very useful for uterine atony (the uterus not contracting following the birth the of the baby). However, I would personally prefer to use Organic Cotton Root Bark for this purpose.
As mentioned in the response above, you dont NEED any tinctures on hand and honestly may be better off not using them if you aren't well informed or comfortable with their indications or how to use them. But these are sort of the basics of herbs most often used for birth. Of course this is only a glossing over of the indications, doses and herbs to use, but I hope it helps :)