I have an Epiphone and a Gibson Thunderbird. It goes without saying, the original design (Gibson) has a lot less "problems" that people associate with T Birds. The Epiphone on the other hand, does. It has worse neck dive, its a bit more uncomfortable to play and wear (Gibson has a scalloped rear), the pick ups aren't the same, the tone is close but not the same, and it feels a little bit heavier.
But its not terrible, at all. Its definitely playable, and though its not as versatile in tone, it does have a nice deep, powerful (albeit muddy) tone that is similar to the Gibson's. Its a pretty good bass for the money.
However.... if you aren't able to play it first (to see if the shape is comfortable enough for you, etc) then starting with some sort of P-Bass would probably be a pretty safe bet.
Having said that, I would still recommend the Epi. It has faults, but its not terrible at all. Can you call that GC, or even another one and see if they have it in stock and go play it. Its the sound and tone of Thunderbirds that makes them so good (to me) and the Epiphone gets pretty close to that.