how to upgrade of iphone4 to iphone 5 on straight talk?

First, my apoligies if this question is answered elsewhere, I couldn't find it and Straight Talk support has not been able to answer my question either. I am pretty noobish at this sort of stuff.

So question.....

I would like to upgrade my aging iphone4 to an iphone5 or 5s. I am on the Straight Talk network.

I understand that I need to buy an unlocked phone but my question is..how do I go about switching the phone?

Is it as easy as transferring the sim card? Will my old number then be on my new phone? Or are there more steps I should follow?

Thanks in advance for any help you might be able to give.