For me the best situations to try to hit a set with low pairs are those where you have a high expectation of value relative to the cost of entering the hand. This usually happens when there are multiple players involved in the hand, which increases the potential payout if I hit a set.
For me, it depends on stack sizes.
I don't go chasing straights, flushes and sets if there isn't a chance of getting paid off well.
So You need to consider the effective stack size.
Position is important, especially with a shallow stack. I'm not crazy about opening UTG with 15BB stack with pocket threes and lots of players to follow. Basically, I'll enter from a spot that (hopefully) avoids a three-bet pre flop.
In tournament play, set mining is most effective early to mid game when deep and the payout can be substantial when fighting against two pairs, top pair top kicker, lesser sets and missed straights.
When you do get there, don't be too cagey or cute. Get the pot growing early so it's massive by the river.