It's all up to your, your budget, and what you feel your skills are.
There are plenty of open source NAS operating systems, just to name a couple...a very popular one is FreeNAS, also NAS4Free, and more media center focused ones like OMV, and Amahi.
As for reusing old parts (computers)...the thing that counts for a NAS is reliable hard drives in good condition. Although many distros support mixing up hard drives, I prefer matching them if I can. Keep firmware on the hard drives up to date.
Spindle or SSD...up to you and your budget.
Some people prefer the "boxed ready to go" NAS units, we prefer Synology for our clients, we usually put the Western Digital RED drives in them.
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