I used to get mad when people said this, but the best chase camera/lens really is the one that you have with you, like to use, and know how to use inside and out.
For DSLRs, the Canon T2i is a solid performer without any huge upgrades in the T3i or T4i - so if the 2 is cheaper, feel comfortable getting it. For Nikon you could probably go with a 3100 or a 5100 and be happy. At the entry levels, there isn't much of a difference in DSLRs. The 18-55 kit lens is not stellar, but more than adequate for someone new to DSLRs. Lens upgrades would probably be like the "nifty/thrifty 50" for ~$100, the Tamron 17-50 f2.8 for a better mid-zoom, and either the Tokina 11-16, Canon 10-22, or Sigma 10-20 (in order of my personal preference). Unfortunately, ISO performance leaves something to be desired at this price point, but oh well. Unless you get to the point where you're looking at $2000 lenses or full-frame, it's almost a toss-up for whether you go Canon or Nikon.
Mirrorless have come far enough you could also consider entering this area. Main drawbacks are autofocus speed, small selection of native AF lenses, and stigma among the dinosaur chasers that think it needs to be 'DSLR or go home'
The Fuji X-E1, Olympus OM-D, and Sony NEX 6 are all kind of expensive bodies - probably a few hundred more than you'd pay for one of the DSLRs I mentioned above. The Fujis have an amazing, yet quirky, sensor that still has some problems in RAW workflows, although it's getting better with every RAW processor release. The Sonys suffer from a lack of amazing first party AF focus lenses, but the body is amazing. The Sony sensors are literally the same ones put in the higher end Nikon DSLRs. The Sony NEX-5R is a sweet little camera that does a lot, and I'd highly suggest playing with one in a store. The mirrorless also have the added bonus of being able to use virtually any lens in MF with a cheap ($20) adapter. Find an old SR mount Pentax in your dad's closet or a Takumar 55 at the pawn store? No problem.
I'd personally recommend looking at the Canon T2i and the Sony NEX-5R, and going out to flickr or something and see what kind of pictures people take and what kind of lenses people use. The gear isn't nearly as important as you knowing the gear, being comfortable using it, and enjoying it. Disclaimer: I used to own a Canon T2i, and switched to Fuji last year.
edit: also, to head anyone off at the pass here "but he asked for the best camera if money weren't an issue!" - a Nikon D800, Leica M9, or Sony RX1 would be pretty cool. A Phase One 645 would be my personal choice for best, though, because medium format is sexy. But you won't appreciate or know how to get the most out of any of those cameras without starting with something more limiting.