This was my third hand at the table, so no definite reads on my opponent.

I'm assuming that his preflop range will be mainly small-medium pairs, most Ax and a few broadway combos, in other words his range is huge.

When he check min raises me, should I just call and reevaluate the turn, or would it be better to shove for protection against any draws?

PokerStars No-Limit Hold'em, $0.02 BB (6 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

SB ($5.09)
BB ($2.41)
UTG ($6.98)
Hero (MP) ($2)
CO ($2.44)
Button ($3.27)

Preflop: Hero is MP with K, K
1 fold, Hero bets $0.08, 3 folds, BB calls $0.06

Flop: ($0.17) 7, 8, 9 (2 players)
BB checks, Hero bets $0.16, BB raises to $0.32

Total pot: $0.49