There are so many websites these days that require you to connect. I've been connecting other wallets with low balances to test things out, but there doesn't seem to be much information around on what is good practice here.
This is a big mistake that was always doing by anyone. They were connecting their wallet to the many websites that they didn't know about what was the reputation of such website.
My big balances are secured by Ledger so I suppose I don't need to worry about the coins simply being stolen without my approval, but what if I connect the Ledger to approve some coins and it steals other coins or uses the approval for something else. Is any of this possible?
Yes it is possible to happen as you are approving the scammers to access your wallet. You didn't even know whether there was a backdoor or not on such platform. That's why connecting to our wallet to the unreputable site is a very big mistake.
When should I not connect to a website?
When you're connecting your wallet to the reputable website and you can do that anytime because it has proven its reputation but you should never connect your wallet to the unreliable website.