Using Tor isn't super likely to avoid trouble with criminal groups (but it won't hurt either). Their main M.O. is to trick people or exploit known vulnerabilities in software and browser exploits are usually beyond their grasp.

Instead they'll try to get you to download some sketchy program, or they'll send an email to trick you into sending them money, guess the password to your accounts, exploit your router and send out spam/malware... that type of thing.

Tor can slightly help in that the sites you visit will likely be collecting less data about you, so when they get hacked and the data is leaked, there's less for the criminals to go through, but Tor is more focused on stopping big companies, data brokers and things like that.

The fact that you your your threat model is evidence that you're far agead of the average person. 💪