I think we all struggle with this question. I've read tons of recommendations via lists from this authority and that authority but too many were elementary or cost more money than my school is willing to pay or I don't want to get it because it costs and I like trying it out before buying it for my ipads.
There are often light versions of apps which allow you to try them out before buying but they often only allow access to the first level or two. You have to pay to check out the locked levels.
I think those lists are a good place to start but you need to know your students. I've made mistakes. I put a multiplication practice app on the iPads and realized later that you just had to type in the x 1, x2, etc in order. The app did not work as I thought.
Before I look for an app, I ask what skill am I wanting them to learn or is this app going to be used to scaffold students? Is it going to be used more to introduce materials or be used for ongoing practice.
Once I've determined the need the app is to meet, I look at the following.
1. Does the description tell if it will meet the need that's been determined?
2. Does it come with instructions so either I or the students can use the app? I've had apps I couldn't figure out at all because the instructions were poorly written or they were nonexistant.
3. Does it have good reviews?
4. Is the cost reasonable? If its a lite version, does it give you a good idea of the locked layers of the app.
5. If you plan on using the lite app does it let you use those skills or does it require you to buy the app at a later date?
6. Is the level such that my students will be interested in using it or is geared for too young a student?
7. Does the app require students to register for their webpage in order to use or does it need to be online to talk to the website?
I've downloaded a bunch of apps that sounded really good but when I tried them, they were not as described. It is important to check the apps out before putting them on the iPads. I tried to find articles on the criteria a teacher should use when selecting apps for the classroom.
To summarize, select the apps which will meet your requirements for your class because you know your students.