It all depends on your personal goals. If you want chickens just for meat and want to keep the price per lb down, order Cornish Cross when needed, raise for 6-8 weeks and be done with it. If you are wanting eggs and meat find a good meat breed or mixed breed or mixed flock.
I personally am trying to raise a good meat breed slowly and have done a bunch of research on breeds and such.
Cornish Cross isn't tasteless, but there is a different taste in letting a chicken age another 6-10 weeks. There's no denying it. It's similar to the difference in grass fed and grain fed beef.
If looking for DP breeds/ heritage breeds that you can continue through natural reproduction Dorking, Brees, Favorelle, traditional standard Cornish, Deleware, Chantecler and Plymouth Rocks are likely some of the best choices. You will get slightly faster growth with mixing these breeds though, which is how they created the Cornish Cross (Generations of trial and error to get the super-fast growth and breast size they wanted.
There is no traditional breed that will have a big double breast like a Cornish cross. Most don't have much breast sadly ( a goal in my personal project) and that is a deal breaker for many raised on store chicken.