Post and Beam sizing for 10x10 shed workshop?
I would consider beefing up the beams a little and going to just four posts.  

Using table 14-40 in this document:   

http://www.southernpine.com/app/uploads/SS_13-14L.pdf  

you can use doubled No. 1 2x10's for a 10' beam supporting 10' long floor joists.  Depending what's available where you shop, if it's easier to get No. 2 grade, you might want to bump up to doubled No. 2 2x12's.    

For the joists - using this table 

http://www.southernpine.com/app/uploads/SPtable7_060113.pdf  

you see you can use No. 2 2x8's spaced 12 inches, or No. 1 2x8's spaced 16", or No. 2 2x10's spaced 16" (or even up to 19.2"), or No. 1 2x10's spaced 24".  

I'd probably buy all No. 1 2x10s because I'd prefer to just use all one size and better lumber is easier to work with.  

I'd use 6x6 posts without even thinking about 4x4s, even if you don't need it for the weight, it's worth it for the additional bearing surface, just makes life easier.