We get this question a lot, especially in more serious cases. Most times, the answer I give surprises people. You would probably expect a lawyer to try to convince you to hire them, but that's always the best decision. There are several reasons for that.
If you qualify for an appointed attorney, you have already established that money is an issue. Unless you have a rich uncle, that means you are going to be limited in how much you can pay a lawyer - which can be a problem. It's probably not a surprise, but the best lawyers usually charge the highest fees. They can do so because they're generally worth it. If money is an issue, you aren't going to be able to hire one of the best lawyers in town. That means you are going to have to shop on price - which is never a good thing. If you need surgery, would you shop around for the cheapest surgeon? If the answer is no, why you should hire the cheapest lawyer when your future is at stake?
Lawyers who charge low fees need a high volume of cases to make a living, which means they have less time for each case. The reason to hire a lawyer is to get someone who can focus on your situation and your case.
I cannot speak for other counties, but I can tell you that in McLennan County, the quality of court-appointed lawyers is pretty good. Even most of the better lawyers are on the appointment list. So the chances are that you are going to get a good lawyer, who is going to work for you.