Any thoughts on how I could/should have played this hand differently? I am not saying how it went down, I am asking how some of you would have played this.
 
I was <20 hands at the tbl. and had no info. other than this session.   CO is Italian and was playing >50%vpip...and loves being the aggressor. This may have been the first hand I had played.

Is my raise here what would be called a min raise?
If it is,how many bb, at this point in the hand, would it take to not be a min raise?

Yes,this is how much I know about NL.   




Everleaf $0.01/$0.02 No Limit Hold'em - 6 players - View hand 1519030
DeucesCracked Poker Videos Hand History Converter

MP: $1.59
CO: $1.88
BTN: $2.56
SB: $1.39
BB: $1.54
Hero (UTG): $2.00

Pre Flop: ($0.03) Hero is UTG with Q Q
Hero raises to $0.06, 1 fold, CO calls $0.06, 2 folds, BB calls $0.04

Flop: ($0.19) A 5 6 (3 players)
BB checks, Hero checks, CO bets $0.19, BB folds, Hero calls $0.19

Turn: ($0.57) 2 (2 players)
Hero checks, CO bets $0.29, Hero calls $0.29

River: ($1.15) 8 (2 players)
Hero checks, CO bets $0.75, Hero calls $0.75

^ Yeah that pretty much.

bet/fold the flop. Give up on the turn. Check calling 3 streets guarantees you of losing the most and winning the least.