Even though you are a newbie, if it were me and I had the confidence to do it; I would do every port. The diving is great! That is the ultimate dive cruise right there. Be honest with yourself, your dive buddies, the dive master - you will be fine. As long as you are in your comfort zone, you will enjoy every dive experience and a good dive master will cater the dive locations to your comfort/experience level.
I enjoy going to smaller dive shops that will give me the customized dive experience to do each port back-to-back. I like ProDive Roatan, in Roatan. Every time I have dove with them it was just me, my husband (my dive partner), and the dive master. In Belize, there is only one shop (as everyone mentioned) Sea Shop Belize. Gypsea Divers in Costa Maya is one of the best dive operations that I have encountered. You enter as a customer and leave as a friend. Finally, in Cozumel, I dive with Scuba Luis. He limits his boat to 6 divers so you have a customized, personalized diving experience.
Trust me - at the end of 4 days, you will be tired, but the memories and experiences will be worth it. You CAN do it.