Unless you find a used bike that has seen almost no use and it is a screaming deal I would keep shopping for a good deal on a new bike. FS bikes have lots of moving parts and these can have surprisingly short life spans, meaning rebuild or replace soon after buying, when you should be able to be enjoying your bike.
Also, there is no warranty on used bikes, and the more moving parts means more that can go wrong, and things like swingarms and linkages are often not available to buy as replacement parts, so if your swingarm cracks you might be SOL (Surely Out of Luck).
I am sure many people have a different view on this than me.