Hating your body isn't a pre-requisite to identifying as trans, really.
You don't need to pursue surgery and/or hormones and/or transition at all. The umbrella is huge and the only way to really get an appreciation for it is indeed to dive right into it; you can do so online, but in person certainly gives a better, stronger sense of what a binary-transcending personal and social consciousness could be like.
Some people find that general "
LGBT" groups don't necessarily help them when it comes to exploring gender-identity specific issues. They may find pressure from the gay and lesbian identified folks in these settings to "stay a gay guy" or "stay a lesbian girl"... etc. Haven't experienced it personally, but heard it quite often; just FYI.
Good luck.