To develop at home, you would need tank and reels and chemicals, and if there's no option for a completely darkened space, you can use a changing bag. The only part that has to be completely in the dark is loading the film onto the reels and getting them into the tank (which is lightproof). The rest can be done in the bathroom in regular light.
But you are right - this just leaves you with the negatives. To see the images, you'd need to either scan them in or print them. Only if you print them will you need an enlarger, more chemicals, trays, or photo paper, and you'd also now need that room with no light in it, and a red light.
That's a lot of money to lay out for a set up if you're not going to shoot a lot of film. I mean, you might end up liking it enough to shoot film more regularly, and if so, then I'd definitely suggest the self-developing route, but if you're just messing around with it once in a while, then I'd send it out. Sparky mentioned Dwayne's, and there's also darkroom.com.
Another possibility is - and this is going to sound bad, I know - is to find out if Wal-mart takes film for development. None of it is done on the premises, but it might be worth it to find out where they send it. The last time I looked into this, they sent black and white film to a place that actually knew what they were doing. I wouldn't trust them with color, but for black and white, it might actually be an option. But you'd have to do some digging at your local store.
If you were in southwestern CT and near the NY border, I'd suggest the place where I take my color film, but you being in southeastern CT makes that suggestion a bit impractical.
Wherever you send the film, ask for scans but don't ask for prints. Waste of money, imo, at that stage of the game. You can look at the pictures easily on the computer and you might want to edit them anyway before you print some, if you print any.
And as a final thought, you might want to google film developing in your local area. The lab that does my film is a little mom-and-pop operation that has been around since 1935. They have the color machine on the premises and do the black and white themselves. These are guys that have been shooting and developing for years. I discovered them years ago when I first started shooting medium format. There might be little operations like that around you, maybe even in places you'd never think of looking.
Actually, I just did a quick google maps search in the general southeastern CT area - Cooper's Imaging in Norwich, CT Prints in Hamden, ABC Photo Lab in Mystic, and a few around Hartford.