Looking into buying a used car. Which cars should I avoid and which cars should I pursue?

I'm looking into the following
Honda Civic years 2005-2010
Honda Fit years 2007-2010
Toyota Corolla years 2005-2010
Toyota Yaris years 2007-2010
Toyota Echo years 2005

These are all potentially very good cars, but any of them could have been abused and on its last legs. Just find one that you like to drive, that fits your wallet, and that your trusted mechanic approves

All the model vehicle you have listed have potential. Initially, they were all good quality and reliable vehicles. The one you should choose is the one that has been fully and properly serviced and maintained through the last several years. If the seller can't provide proof of all service records you need to keep shopping.

You should be safe if you stick with Honda, Toyota or Nissan products.

Pursue the Toyota Corolla and Honda Civic