Your play until the turn seems fine.
Turn - bet $1.20-$1.50 here, this is a great card for you, all draws missed! Dont bet small to get villains to bet into or bluff into us as this wont happen enough to make your play +EV and will price in all drawing hands.
River - I like check-calling here! If we bet $1.20-$1.50 on the turn this leaves us with about $2, so we can profitably call if we check and he shoves. This river card again is a brick, we are only paying off a flopped set, A8, K8 and 78. Basically I think villain will bluff enough on this brick river card enough to make a check the best play! If we were to bet for example would we get called by anything worse than our hand? No, check and hope he bet/shoves
Villain had 9T or K4 clubs btw