Will a Radeon HD 6870 be bottlenecked by a PC with the following specs?
Intel Core i5 2500k
Crossair Vengeance 8Gb DDR3 1600 RAM
ASUS P8Z77 LK Motherboard
NZXT HALE82-N NP-1BN-0550A-US 550W ATX 12V 2.3 Power Supply
If it does, which card would be best suited for this rig?
A 2500k probably won't, with a mild overclock, bottleneck two or three Radeon 7970s. You're more than fine. (Though both sandy bridge and the 6000 series draw a lot of power... I'm withholding advise on that till someone more knowledgeable with those parts comes along, though. I skipped that gen of tech.)