Looks like you won't get away with using a ~300W PSU on either card.
http://www.tomshardware.com/reviews/ati-r680-rage-fury-maxx-2,1764-17.html
Tom's hardware recommended at least 450W for the AMD HD 38720 X2 and GTX 480 had ~250W just for itself.
I sometimes make computer packages from older parts for relatives who are already retired. Usually Linux Mint or Windows 7 serves them best. One of the best projects is a computer I used myself for around 4-5 years as a Windows XP/Linux computer. It's served as the home computer at a relatives house for almost 10 years now, good enough for youtube, photos, facebook. I've asked them if they wanted a newer computer but they're satisfied after they switched to Linux. I expect it to last at least the full 20 years using mid-range parts. Only thing they've needed change is the CMOS battery (twice) and speakers.
Way ahead of ya, bro
The PSU's I have are one 460W and one 480W. Expected, since I'm all for the more future proof approach, tho I admit I failed in this many times.
The problem I feared the most was the +12v rail(s). Luckily, connectors and amps were sufficient. I managed to run the HD 3870 X2 just before I came here to report back.
My fear I mentioned before turned out to be real... but solvable unlike the case with the 7300 GS before it. AMD's driver was flexible this time to have the Win8.1 driver run on Win10. Outdated, but made perfectly optimized to utilize the card reliably before it got discontinued, as I read on AMD's logs.
I even tested it on Resident Evil 6 Benchmark Tool and the dual GPU feature worked perfectly. I got a max. of ~70FPS, an average of ~40FPS and a min. of ~10FPS (normal, since it's a stress test to, not a reflection of a real game play experience) which is impressive for a system this old, and very playable. The 3870 X2 is a Q1 2008 and the CPU is a Q1 2009. The computer is +6 years old.
The case is similar with the other card. This experience turned out to be 99% successful