The signal bars will not be meaningful until the phone is activated. This is my understanding.
You can use whichever model phone you want, as long as you know that you will have coverage. Tracfone steers you to certain carriers for their business advantage, not for your business advantage. But, TF does not have unlimited privileges with the carriers. There are just so many new numbers that TF is allowed per market, so you might have to follow TF's guidance if you need a new number. And sometimes they won't let you bring an existing number into a market. This is all controlled by the carriers. But these problems are rare in larger markets where carriers are trying to steal customers.
There is a trick to seeing particular Tracfones. When you put in your zip code, look at the url bar. T-Mobile will have market=GSM5. AT&T will have market=GSM4. Verizon will have market=CO. Try COGSM4 for a combination. You can change this to the other and see different phones. Just make sure to hit enter to refresh the page. It doesn't matter which page you order from, it is irrelevant to the shipping address. A mismatch doesn't matter, because people buy phones for other people.
Zip code matters when you are activating the phone with a new number, so that a number local to that zip can be assigned. It doesn't have to be your home zip, either. You might have a reason for wanting a different one. As long as there is coverage.