What's the best: Toyota Corolla, Mazda 3, or Mazda CX-3?

So many options. It's great to hear that you have had such a good run out of your Corolla, and that you would happy with another one. The Corolla is certainly a good option. So too is the Mazda 3, which would satisfy all of your needs. Both cars would be good choices. The Mazda CX-3 is a different car in that it is an SUV and gives you the advantages of a high driving position for good visibility and the flexibility of a wagon style body. It too would be good option, and I would suggest that you had a test drive of it to see if does what you want. All three are well built, reliable and I would expect them to give you many years of good service.