If you want to go the budget route I would keep the case. Internal parts are subject to problems over time. For this reason most builders just replace them to avoid future problems, even if they worked on the old system. Old style hard drives which are spinning a platter every time you use them are subject to mechanical wear.
Re using the old power supply would be iffy but might be possible if the current drain on the new parts isn't over loading it.
Most vendors have matched cpu/motherboard combos already picked, so when you order the set you know it's compatible. You could order one of those with a new hard drive and OS,memory.. cross your fingers and be on your way.
One of these recent threads had what I thought looked like a crossover mobo from AMD with the PCI slots so you could keep your M-audio card and also had usb 3.0. Really though, PCI is on the way out. If you aren't planning to keep the card for much longer why bother?
I wrote an article on building your own PC at my website, but if you just don't want to build it yourself I understand.
Total cost with DIY upgrades would be-
Mobo cpu combo
at least one SSD
New OS
16gb memory
new usb 3.0 interface
amd is less expensive. For simple recording you wouldn't notice a difference. Maybe some AMD people can chime in. I normally would recommend Intel but if budget is a real concern many have successfully built amd systems with no issues. My first build was an amd and I never had any trouble with it..