A properly-applied sunscreen will be a thick layer over your skin (most people apply way, way too little sunscreen). So thick that it will mask the mosquito repellant. So most health websites like the CDC suggest the sunscreen first, then the mosquito repellant.
Plus, that mirrors how you should apply it anyways. Sunscreen needs a half hour to start working, while DEET works right away. So, you should apply sunscreen well before getting outside and then DEET just as you get outside.
Finally, DEET is a vapor-based repellent. DEET confuses the mosquito's sensors. They only need the vapor near them to get confused. You don't need to actually apply DEET to the skin (your clothing works quite well for that purpose). So, I like sunscreen on the skin and DEET on the clothing. Once a mosquito is on your skin, you've likely lost that battle and DEET there won't do you any good.
That said, I highly recommend seeing a travel nurse. Get your malaria pills and any vaccinations you probably need BEFORE getting sick. While you are there, any good travel nurse will stock you up on Permethrin. I personally don't even need DEET when wearing Permethrin treated clothing. Finally, they can stock you up with antibiotics that work in your specific destination so that when you get stomach problems, you already have the treatment handy without sitting in a 3rd world health clinic crossing your fingers.
Edit: listen to EliteRetard, he knows his stuff on this topic.