It really depends on how big and active your forum is. The actual installation at the beginning doesn't take much space at all. I don't remember even the general size, but free hosting handled our test forum just fine, and we tested it well. 
However, this AO forum is BIG and we've had to upgrade the hosting package a few times as it has grown.
However, this AO forum is BIG and we've had to upgrade the hosting package a few times as it has grown.
Phyllis in Ukraine, with Jaan (AO grad), Raia (AO grad), Asya (age 17), Bogdan (age 14)