Just choose one.

You may have several I20s at the same time. When you file petition to transfer your status to F1, you can only stick to one school. Besides, you will need the help from the ISO of school you want to to help you to file the transfer. Then you'll have a better chance to get it. As for the other I20s, you can just return them. The status transfer depends on your situations mostly not on the school you are going to, unless for some very special reasons or fields or school they don't think it's a normal school.

Your situations like: what's your current status ? Do you have any status gap ? Do you have enough funding to support your study ? Besides, you need to write a statement of purpose to indicate why you want to transfer to F1. Why you didn't aplly for F1 visa when you came to US ? Any good resaons to let them believe you'll go back whn you finished your degree ? That's why you need to go through the ISO of your new school. Normally, they will provide you a checklist required for the transfer and check yur documents to make sure it's a good package to file for transfer.

However, if you are on H4 now, there is no need to transfer to F1. You can go to school full-time or half-time whatever you like. Besides, some schools allow H status holders to pay in-state tuition. Unless you want to get assistantship or apply for OPT later.