What is bottlenecking, and will it happen to me?

Your FX6300 can handle a lot stronger card so we could say that the HD7750 is bottlenecking it.

The HD7750 is the best I can get for my budget, but it isn't holing it back too much is it?

No bottleneck will happen except some games were intel cpus perform better then amd. Bottlenecking is when 1 component limits the other component(s) to stop it running from its full potential.

GPU z and gpu load in games is best way to measure it and task manager cpu utilisation. 99% gpu load means that you are fine with no bottleneck. Lower cpu usage means you have a decent c[u ready for even more higher end graphics without bottlenecking it.

Thanks, I'm on a budget, and if I feel like spending a bit more, I can get the Radeon HD 7770( only 1GB, not 2) would that be better? I CANNOT afford any nVidia, (plus I hate them, and have had many problems with them in the past)

HD7770 1gb will be faster than HD7750 2GB but really people are more worried about when the bottleneck goes the other way, that is CPU holding GPU back.