So, I lost money on this hand, in my opinion by poor betting. I called from BB w/ a marginal hand, but it got better. My immediate deconstruction is that I should have pushed hard as soon as I got the set, but how hard? What is the *right* play here?

Raise when I turn up the pair?

Push hard when I complete the set?

Slow down when there's a flush possibility on the table?

PokerStars No-Limit Hold'em, $0.05 BB (9 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

Hero (BB) ($7.81)
UTG ($5.35)
UTG+1 ($9.43)
MP1 ($3.61)
MP2 ($2.16)
MP3 ($9.54)
CO ($10)
Button ($1.70)
SB ($9.90)

Preflop: Hero is BB with A, 3
2 folds, MP1 calls $0.05, 3 folds, Button calls $0.05, SB calls $0.03, Hero checks

Flop: ($0.20) 6, 3, 2 (4 players)
SB checks, Hero checks, MP1 checks, Button bets $0.10, 1 fold, Hero calls $0.10, 1 fold

Turn: ($0.40) 3 (2 players)
Hero bets $0.11, Button calls $0.11

River: ($0.62) J (2 players)
Hero bets $0.97, Button calls $0.97

Total pot: $2.56 | Rake: $0.10