Black and white printing was actually a higher hurdle to jump; inkjets are clearly the method of choice for color printing and have been for a while. The gamut provided by Epson K3, HP Vivera and Canon Claria inks all exceed that provided by Noritsu/Lightjet type printers on Fuji crystal archive paper. The vast range of papers provide endless aesthetic options not available with the photochemical digital printers; and archival longevity of pigment inkjet prints far exceeds that of any photochemical process.
Paper thickness is whatever you choose to print on. Larger printers in the Epson 3800/7800/7880 class give you a wider range of choices; the 2400 doesn't handle really thick papers as gracefully.
As far as specific printers go, your budget is the real issue. The Epson 3800 is pricier than the 2400 up front, but comes with much larger ink cartridges and cheaper ink costs in the long run, and lets you print up to 17" wide. HP's 13" carriage B9180 also prints beautiful color and BW work. Larger 24" wide format printers give you lots more paper options and print much faster, but obviously take up a lot of room and cost a bunch more up front. They're cheaper to run per-print, however, due to larger ink cartridges. Epsons seem to have more clogging problems than other brands, but I've left my 7600 sitting for several months and only had to do one round of head cleaning before it printed just fine.
Time to print a 13x19" print depends on the specific printer; bigger is faster. Even for the Epson 2400 at highest quality setting, it takes about as long to run off a 13x19 as it does to get coffee. Cost per print again depends on the specific printer; a quick back-of-the-envelope estimate for my work is about $2 worth of ink for a 13x19 from a 13" wide printer, about half that for a wide format printer.
Just my 2 cents, if you're looking for the most economical printer up to 13x19" at this point it's probably the Epson 3800, given its larger ink carts. Its output is also superb, as good as anything out there. The newer 7880 generation with Epson's "vivid magenta" ink has a modest increase in the already excellent color gamut. Among larger 24" printers, you can't go wrong with Epson, HP's Z3100 or Canon's IPF6100.