What memory do you already have in your system?
Since you say that cost is an issue, what do you do that requires more memory and how much does it require?
If you have a 32 bit OS, it will only recognize 3 t0 3.5 GB of memory. More is ok, it will not stop it from working, it will just be ignored.
If you mix memory speeds, it will all run at the speed of the slowest stick.
The answers to you other questions depend in part on your answsers to my above questions.
what processor do you have ?
because if it's not a powerfull enough processor, it just won't be able to use that much memory
6Gb is just useless (if your motherboard even takes that much)
you would be able to boot up wich 6Gb but under a 32 Bit OS, you'll only be using 3Gb
I can't even think of any program needing that much memory ...
I guess I wanted to have so much memory under my 64 bit OS that pages wouldn't have to be swapped to disk.
In some places, I've read that if you mix memory speeds and sizes, everything should work, only the speed of your slowest memory will be used. In other places, I've read that your system may not even boot. Memory sticks should be matched to the greatest extent possible.
You may have to disable the auto-detect feature in the BIOS and manually set your memory to whatever the slowest speed memory is before adding memory that is different. Some boards seem to have a problem with getting the settings right on "Auto" when different speeds and timings installed, causing a no-boot situation.
Some motherboards are sensitive to differences in memory, and some are less so. In any case, mixed memory will work at the lowest common denominator in speed. They should also be able to run at the same voltage. To get dual channel operation, the sticks must be balanced across channels in capacity and configuration.
I would look to match the sticks as best I can, from corsair.