how much, impact it has on performance of the actual computer
If bus speeds, CPU and everything else are equal, I would rather have 4Gb of slow RAM than 2Gb of fast RAM. And I recommend 4Gb bare minimum, ideally 6Gb with triple channel memory architecture and 8Gb with dual channel architecture.
but has a budget
You want a decent amount of RAM. If your budget allows for faster (more expensive!) RAM, invest that money in better graphics - you will likely get more bang for your money. If budget was not an issue, then sure, faster RAM will yield better performance. But before faster, you must have enough.
And remember, a good PSU from a reputable maker is a must.
32-bit is history and will hold you back. Go 64-bit - even if getting 4Gb or less of RAM.