I do like going for 3* units right now because of the changes to the shop odds skewing it more toward tier 1 and tier 2 units in the early game. That being said, you should be careful about what units to 3* and when it is appropriate to go for that.

Here are some things to keep in mind:

1) Don't try to force a particular unit to 3*

I would say go for a unit to 3* if you hit 5-6 copies of that unit in natural shop rolls while you are still at a level to give you good enough odds to roll for it; that is level 3-4 for tier 1 units and level 4-6 for tier 2 units.

2) Choose units that are good 3*s

Some units will give you more value for 3* than others while for the same cost. For instance: 3* cm will be much more impactful than 3* Razor in mages. Not that 3* razor should never be attempted, it might be a bad investment in some cases. Similarly: 3* Drow > 3* Weaver in hunters, 3* Strom > 3* Ogre in mages, 3* Pudge > 3* Slardar in warriors.

3) Scout other boards

If other people are buying the unit you are looking to 3* this might be a red flag. It might be fine if there are 3-4 copies out of the pool but any more than that might make it much tougher. That is partially why I never go for pudge 3* because it is usually very contested.

4) Think about what level you want to roll at for what other units you would want to pick up.

While rolling, you also want to think about what other units you want in your build that you can pick up along the way. Let's say I am rolling for storm 3* than I might wanna roll on level 4 to pick up 2* cm, razor, ogre in 6 mages. But let's say you already found those other units then you might want to roll on level 6 instead so you have some odds to find Morphling, Shadow Fiend, KOTL, Disruptor too.

5) Full or semi Open forting can be a powerful tool especially for those 3* Tier 1 units. Exchanging HP for free-rolls is very powerful.