Steam Question

[P-Sleazy]

Sooo...I'm about to crash my computer and reboot it to factory default settings (mostly to fix alot of default programs I seem to have inadvertently "broken" over the years of tampering with computer files and options and etc). Anyways, I'm putting a list together of everything I'll need to recover (mostly, as it turns out, this list is comprised of videogames...how ironic!). So, my question is, will I get all my games back onto my computer when I reinstall steam without me having to pay for them again? Also, for when I buy a new computer a few months/year down the road, can I transfer said games onto that computer aswell?

Thanks in advance!