What one of these is the best?

Generally speaking, the Ivy Bridge CPUs are about 6% more power on average compared to Sandy Bridge assuming the same clock speed. Will you see that extra 6% increase in performance in normal everyday usage and games? No, but it's there.

Models ending with the "5" has the better integrated graphic core. If you are going to buy a graphics card anyway, then it does not really matter. If you intend on using integrated graphics for playing games, then it matters. However, they are not very powerful and are generally only good enough to play games at low resolution.

CPU Model #___________Integrated Graphics
Core i3-2120___________Intel HD 2000
Core i3-2125___________Intel HD 3000 (About equal to Radeon HD 5450)
Core i3-3220___________Intel HD 2500
Core i3-3225___________Intel HD 4000 (About equal to Radeon HD 5550; 35% more powerful than the HD 3000)

So if I am getting a graphics card, the best would be i3-3220 or i3-3325? OR would it be one of the other two?
I am also on a tight budget!

i3-3220

The i3-3220 has a 512 kb L2 cache and 3mB L3 cache while the i3-2130 has a 5mb L2 cache and 3mg L3 cache. Does this make a difference?