Breville Bambino

It'll be a pain in the butt if you don't like the ritual of it. If you don't want manual, it's probably around $600 for true quality espresso with a Breville Bambino and Eureka Notte or Sette 270. That will give you good shots and also has the milk frother if you ever want it. A good chunk of change though.

You also need a good grinder. The cheapest grinder option is the 1ZPresso JX Pro which is a hand grinder. You won't be able to afford an electric grinder at your budget. If you want a machine that can also steam, the cheapest option is a Breville Bambino.

If you want semi-auto, then the cheapest you can get good results with is the Breville Bambino (base model not Plus) for $300. You will need to upgrade its pressurized filter basket to an unpressurized one (Breville calls it single wall).

Get a Breville Bambino (base model, not Plus, for $300). It will work much better than your Mr Coffee ever did. It comes with a pressurized filter basket so it will work with pre-ground, or coffee from most burr grinders.