What everyone said.
Hooking up with the nearest club is the single best thing you can do as a first step. Most clubs will happily mentor you if you ask, which means no initial equipment cost beyond safety gear (faceshield, not goggles. wood hurts).
I'd strongly recommend, if you decide to jump in, getting a Jet Mini (non-VS, saves money and works just fine) as your first lathe. It's a bomb-proof little bugger that will turn an amazing amount of stuff. A large minority of turners in my club own one, most clubs have them as their demo lathes, and I don't know of anyone who's sold theirs when upgrading. It's just such a good little lathe, I'm not sure you can damage it without purposefull effort (short of dropping it in a lake, and I'm not sure that would work) and you're always going to be turning small stuff in addition to any big stuff (9" swing).
The other suggestion would be that, if you have any trepidation regarding waving goodbye to your general woodworking hobby, run, don't walk, away from woodturning. So many folks, including myself, now use our table saws as storage space and our bandsaws for resawing green wood. It's just kinda sad, all that good equipment now gone to waste.
Good luck,
dietrich