A standard 400w PSU will do matter which make it is. There's no such thing as "good" & "budget" combined in one sentence. You get what you pay for these days. My PSU cost me £35 but is silent & 600w with LED's & 2 fans.
Any decent computer shop will stock standard 400w PSU's.
Personally I'd test the PSU prior to replacing it & check the HDD for errors as there may be a bad sector? You can buy a PSU tester quite cheaply, I swear by them
PSU's operate on 3 levels of power so a tester will prove it one way or another.
As for the errors, there'll seem like there's no blue screen as it flashes up in a split second as XP restarts by default. Try starting in safe mode (press f8 after the post beep) and go into system properties - advanced then start up & recovery - settings - & untick the automatically restart. Then when you reboot it'll show a blue screen if there is an issue with XP, HDD or drivers etc. The error code will then be visible & you can take it from there. It'll look something like this; STOP: error code 0x00000024 ...... or similar?
Sorry if thats off the mark but my experience tells me it's HDD or software related & possibly a corrupt NTFS file system (stop error 24 as above).
Good luck & if you get stuck I've got spare PSU's which I can post to you if you pay the postage