Just some more thoughts. If bagging rabbits are your main interest, there is not a much better dog to go with than a beagle from proven hunting stock. My late father trained and hunted rabbits with beagles for almost 60 years. He even played around with the field trial scene some and came up with 4-5 Field Champions. Lots of folks seem to think a "pet" will not make a "hunter". Not so from my experience. Dad never had a big kennel. Usually 3-4 at most. All were his big buddy pets. A few were as good as I have ever come across as far as hunting. Never saw one of his catch a rabbit, except the occasional one that had been wounded.
I got into Dachshunds some 20 years or so ago. First as a pet. My second one , Tex, was a more or less self trained treeing squirrel dog .... and one heck of a "blood trailer". I can count on one hand over the 12 years he blood trailed the number of bloodied deer that he did not find. And that has been the case with Mojo and now Ellie Mae. All three of these pooches are 100% pets and 100% hunters.
So go ahead and get you a hound pup. Doesn't make much difference which breed, or even some sort of a cross. Take it to the rabbit woods every chance you get and treat it like a buddy too. But be prepared to put in the time. Get the pup on rabbits every chance you get. Even the "naturals" who don't require much training need to know what pleases you.
And as already mentioned, be sure you understand the hunting and trapping laws or you may find yourself looking at big fines.