I have two PC3200U modules and two PC2700 DDR modules. My mainboard supports both types and has 4 slots which are each color coded. So if I put each pair in the slots of the same color I'm good right? Would there be a performance increase if I used the exact same RAM modules like 4x PC3200 or 4x PC2700?
The RAM will clock down the faster RAM to the speed of the slowest stick that you put in, so yes, it will still work, but you won't be getting the most out of your RAM. Your best bet is to put in sticks of matching RAM if possible. Your performance for 4x PC3200 would be better than 4x PC2700. If you put in 2x PC3200 and 2x 2700, it will be like running 4x PC2700.
If you want to know how to put RAM into your computer, check your motherboard manual, or post your motherboard in your post so we can help you out.
As has been pointed out, your system will downclock all RAM to the highest frequency supported by all installed memory modules. Some motherboards also downclock RAM just because they can. (Populate all four slots on the Asus M5A97 Pro for example, and it downclocks the RAM even though all modules support a faster clock...) Hence, while there should be no compatibility issues assuming your motherboard supports all the memory modules used, you won't get every last bit of performance out of the faster RAM if you mix faster and slower RAM, but it won't (shouldn't) be slower than what you would get by using the same total number of modules of the slower RAM.
However, it's worth remembering that simply installing more RAM will often in itself give your system a fairly noticable performance boost. This is because:
The system won't have to resort to swap as often, as more code and data can fit into main memory (reducing the need for disk I/O)
There is more free memory to use as disk cache, which will speed up disk I/O for anything that has been accessed recently (which with a large disk cache is more than you might imagine)
Which one of these becomes the dominant factor depends on whether your system is RAM constrained before the upgrade, but either can give the system quite a boost in actual use except perhaps for some highly specialized workloads (and if you're into those types of workloads, you probably wouldn't consider mixing RAM just because you happen to have a set of DIMMs on hand).