Well for the $ the 6870 is a good GPU to get. The 560 is on par with the 6870 and consumes a bit more power and generates some more heat (depending on design of the GPU of coarse). The 560Ti is good too, but costs about $70 more than the 6870. So for the price/performance and at your resolution the 6870 is the winner, if your going with those 3 options.
Personally if I was considering other upgrades, I'd consider getting 4 gb's of DDR2 (total) and possibly than upgrading the Monitor to something with 1600 x 900 resolution or better. But this is just my opinion.
I think your best upgrade path is getting the 6870 GPU w/an additional 2 gb's of DDR2, so you'd be at 4 gb's of DDR2 and have a good GPU too for about the same as the 560Ti GPU
Edit: Just checked out your mobo specs, and you'd need to buy 2 x 2 gb sticks to get 4 gb's or RAM, since your mobo only has 2 DDR2 RAM slots on it. 4 gb sets (2 x 2 gb's) are going for about $50-70 here in the U.S., so I don't know if that would fit into your budget, but I'd seriously would consider upgrading the RAM to 4 gb's too. You didn't mention what OS your running on, but if your on a 32 bit OS (Windows XP/Vista/7) than you'd only be seeing about 3-3.5 gb's of usable RAM. Upgrading to 4 gb's might not be as effective of an upgrade with a 32bit OS, but it would definitely help out.