I'm looking at putting together a server as follows:

Fractal Design Node 304 chassis
H67 miniITX motherboard
Intel Core i3-3220 (Ivy Bridge, 55W)
8 GB DDR3
64 GB SSD
5 x 3.5" HDD (2 & 3 TB)

Is there a picoPSU that could power this? If not, what would be a minimal, but safely sized ATX PSU?

Maybe I should add: As a media server, there would seldom be more than one or two HDDs spinning. However, I don't believe I'll have any means of staggering drive spin up when powering up the system.

I think pretty much any system deserves something like the Seasonic G-360 or better as long as it fits, as it does here. Check around for prices and see if it's not too expensive for what you had in mind.

I've tried adding drives to my file server; five drives work, six does not. So a picoPSU could work but I wouldn't recommend it with that many HDDs.