I think the most important thing about a doula is that her personality and style complement yours and your partners. For my DD's birth we had a doula who was super-nice and we got along really well and I was very comfortable with her, but when it came down to it her personality wasn't quite forceful enough - I can be...difficult, let's say, and I needed someone to give me a stern talking to as soon as it became apparent that my baby was posterior and I was suffering a lot with back labour. If I'd had a more experienced doula with a more authoritarian attitude who could have got me positioned better and actually working on it, I think I would have felt better even if the outcome had been the same. But I curled up in a little ball and made moaning noises and my doula patted me on the head and sympathized. That might have worked really well for someone who wasn't me. This time around I've got a doula who is 20 years older than me and way bossier. I might get heartily annoyed at her, but she'll give me the goods when I need it!
It's hard to say when it's your first and you've no idea what you're like in labour, but think about the hardest, most stressful times in your life - what sort of "coaching" worked best for you? Do you respond better to gentle encouragement or "suck it up, princess" tough talk? Do you want more involvement, or do you want to go it alone? Is this support more for your husband or for you? (It is TOTALLY fine - great, even - to hire a doula predominantly for your husband. Our doula did do a fantastic job of keeping DH settled and sane through it all.)
Post-partum, if you have difficulties, it's best to hire a post-partum doula. Most birth doulas provide some post-partum visits, but they won't be at the level a post-partum doula can provide. I may be biased, here, being a post-partum doula myself - but my visits are usually 4-5 hours, include some child care so mom can have extra sleep, breastfeeding help, heavy-duty laundry, food preparation, light counseling for both parents if needed (often there's stress and tension) and referrals to other professionals if it seems like a good idea. I also accompany moms on first outings after baby or to midwife/dr visits if the mom isn't comfortable going alone. Birth doulas often don't have the time or schedule flexibility to do all this, and honestly a lot of them do births because they love the process of birth and all the drama and wonder and everything that goes with it... I avoid them for the same reasons - I love watching mom, dad and baby get the hang of life together and as I typically work with families for several weeks to several months, I get to see the babies grow and change and see parents' confidence grow as they get to understand their baby's personality. And, too, much of my function is to provide adult conversation that is completely ok with the only topic of conversation being the baby at hand. Mamas LOVE to talk about their babies. Their friends either have no babies or their own babies and keep wanting to discuss THEM - but I am there to talk just about THAT baby. Weird as it sounds, that's what's needed. And I don't mind a bit. I can answer all the "is that normal?" questions and the "how do I...?" questions in the context of this particular family group and I think it's a lot less stressful for mamas than going to a baby group or hanging out with friends and hearing a lot of "well *I* did this" or "we didn't do that". But, that having been said, all of what I do is stuff that ideally, would be done by a close relative or friend - unfortunately many people in our culture don't have someone like that to call on nearby. But if you do, that's great, and by all means use them! I was actually inspired to become a post-partum doula after my MIL took such great care of me & DH after DD's difficult birth. She came over and did laundry and made us sandwiches and chatted endlessly about the baby - she knew bugger-all about breastfeeding but was as supportive as she could be nonetheless and she basically saved my sanity and prevented my PPD from becoming truly debilitating. Afterwards, I wondered how people got through it all without a Beverley... and found this concept of post-partum doulas!
Sorry, that's a bit of an essay. The main point is that if you don't have a lot of support and you and your partner have a hard go of it adjusting, a post-partum doula is a really, really worthwhile investment.