I don't know about Windows 7 but you can near enough double the speed of a new Vista PC with basic optimising.
Named brand PCs will be heavily loaded with utilities, free software etc. All those fight for resources - especially at startup.
Vista has to be the most insecure O/S ever. I don't mean as in security but in the way it looks after itself. Vista has OCD.
Vista tries to confirm, re-affirm and log EVERYTHING it does It even logs when it is logging. No joke.
If you turn off most of the logs, unecessary services, tune the memory you could see a doubling in speed.
Consider SSD. These are much cheaper and more reliable now and will really make a difference.
Note that there are some older generation SSD out there so make sure you have the latest (read / write speeds of around 200MB/s, the older types are around 90 to 150 MB/s)
Get a normal hard disk just for backups.
As already stated you will be limited here by the O/S. If 32 bit and XP or Vista you won't get more than around 3.5Gb to work.
Go for a motherboard with the latest DDR3 memory. This will be the fastest / give best bandwidth.
You can get PCs with onboard graphics but this is not ideal as unless it has it's own dedicated memory it will take RAM. Best option is to purchase separately a cheap PCI Express card for around $40.