But generally people don't choose the 5DmkIII or 1DX because of financial limitations - and needing to keep sufficient funds for decent glass.Yes. If money is no object, go with FF. But APS-C cameras today are also amazingly good today, and the price differential is substantial. I've been shooting with APS-C for a decade or so (when did 10D appear?), last four years with 7D, only getting my first FF (5D3) this year, and while it is clearly better, I have no regrets about not doing it earlier.
In particular, I like the EF-S 17-55 very much, and given your comments about your budget that's what I'd get, with whichever crop body (550D or newer) you can get cheapest - image quality won't change much (if you shoot raw - jpeg engines are better in newer ones). I'd prefer the 60D because of the top LCD and even more because I'm addicted to the back wheel, but for most people it doesn't matter so much. (The 7D is superior mainly if you shoot fast-moving subjects, like wildlife or sports.)
But what suits me might not suit you. Given a limited budget, with APS-C you can get more lenses (and accessories like tripod and flashes) that will cover wider range of situations, but image quality will not be quite as good as with FF. If you are one of those people who only want perfect pictures rather than wanting at least some kind of picture in wildly varying circumstances, you might be better off starting with FF; especially so if your main game is low light, because that's where FF advantage is biggest.