This is my preference too - mainly feature tests, and unit and integration tests where they provide enough value to be worthwhile. I generally end up with 70-75% test coverage, but I don't pay too much attention to the actual number.

We just released a fairly large system that took this testing approach - despite a large number of tests hitting a database, file system and a blob storage emulator, they still completed in only 5 minutes or so on our CI machine (or 1 minute locally on very beefy laptops).