How many friend slots do you start off with, and how many do you get per Steam level?
As per this Steam forums thread, and this Community discussion:
By default, you have a limit of 250 people for your friends list and every level adds another 5 slots - which means that you get 50 slots per milestone (10, 20, etc).
In addition to that, linking a Facebook account adds another 50 slots - to a base of 300.
According to the bottommost entry of this page, the initial limit is 250 and the answer to "What do I get when I craft a badge from my Trading Cards?" on this page says that each level increases the limit by 5.