When we slaughtered our first batch of rabbits I was worried about how we would all react, but it went surprisingly well. It was a family affair for us, and everyone had a job. DS1(14) brought the victim out to a small surround we made which was placed on a clean rubber stall mat. My hubs shot the rabbit with a pellet gun. Once it stopped twitching we hung it on slaughtering hooks, DH cut the head off and then everybody looked at me (Mom!) and said "Okay you show us how to do the rest the first time.", and even though I hadn't done anything but read about the process, I was voted most qualified. So I made the cuts around the hocks and anus, cut off the front paws with pruning shears, skinned it, then opened the belly and gutted it. I couldn't get the heart and lungs, so my DD (12) volunteered and dug them out. She asked to skin and gut the next one. Our DS2 (9) rinsed the stall mat clean between bunnies. My daughter and I scraped the skins, rinsed them, and put them on hide stretchers. The carcasses were put in ice water to cool and later I quartered and froze them. I didn't know they were supposed to age in the fridge for a few days to get past rigor mortis- and when I cut them up they were stiff- but once thawed from the freezer, the raw meat resembled chicken and had lost that stiffness.
When we were done slaughtering, the kids asked if we were having rabbit for dinner, and my DH said "No-o-o... not tonight." A couple days later I defrosted one and we cooked it for about an hour with Pace Picante sauce, shredded the meat, fried up some taco shells, and served with chopped onion and cilantro. It was delicious and we didn't have to stare a bunny drumstick in the face on our plate. That made our first meal easier (for the adults at least!).
If you can, get some friends to help process your first batch because then you wont feel like such a ghoul. A friend of mine raised turkeys one year and we had a "slaughtering party" on Xmas Eve and it made it a lot easier than if we had done it solo. Also, the more you do it, the easier it gets... we helped prepare a friend's steer for the butcher recently and it didn't bother us- in fact the kids (ours and theirs) artfully arranged the skin, head, and lower legs once they were off. So if you ask farm kids, slaughtering can be fun!
The most important thing to remember is that once it is dead, you can't hurt it anymore, and it is no longer a rabbit or goat or cow- it is meat.