How badly will my cpu bottleneck?

CPU: Specs: AMD A4-6300 APU
GPU: AMD Radeon R7 260X
8 GB DDR3 RAM

What games will I be able to run, and at what settings?

Added (1). 5 Games (For example): CS: GO
AC IV: Black Flag
Dirt 3
Project Cars
Minecraft

Added (2). Just Cause 3 instead of Minecraft.

You should be able to play most new games at about medium settings. But I wouldn't count on being able to run them at 60FPS. Mostly because the outdated Graphics Card with a limited memory of 2GB.
Older games, though, sould run a bit more smoothly.

Most gamers do not know how to predict bottlenecking, and ignore the weak cpu.
I checked Skyrim using game-debate.com CAN I RUN, which is best source available.
With A4-6300, which is 53% of recommended, and GPU@163% and RAM @ 200%
Medium-high 1080p 35fps
http://www.game-debate.com/...quirements
with athlon x4 860K - highest CPU that fits the socket, but may or may not be compatible, CPU at 115% and runs ultra settings estimated 57fps 1080p, verified in youtube reports with a strong CPU.
Graphics ram has been proven irrelevant over 2GB except at ultra settings of modern games maximum textures. Dedicated video ram importance is overstated.
You have to name your games to see the % of recommended CPU/GPU/RAM to estimate game play via sites that look at it. Name 5 other games.

I think there be little bottlenecking if kept playing modern games at low to medium settings, getting into higher settings is when the bottlenecking will start getting worst