My gaming PC is connected to my TV and I sit about 6ft away to play. I typically play single player and with a controller, but would like to try out Civ and some other keyboard-needing games. My current keyboard/mouse are pretty old, and lose connection pretty frequently. Can you guys recommend a wireless or bluetooth keyboard and mouse that would work well for my scenario?

Logitec MK520 is very nice and around $30-$40:

Logitech Wireless Combo Mk520 With Keyboard and Laser Mouse

If you play a lot late at night and if you don't mind spending some money, you may want to get their backlit keyboard, the K800, and buy a separate mouse.

If all you are looking to play on PC is Civ and other non-action games (e.g. shooters), then you can get the Logitech K400 for $40. It's a small wireless keyboard with a touchpad. Better to have an all-in-one solution to keep your coffee table looking neat and tidy.