I am having a bit of trouble deciding what sort of exercise to do first. I am just slightly overweight, so I would like to lose weight. But I also want to become flexible so that I can get better results in a medical test that I will have to do at some point. So what would be better for me to do? Will Exercise help me become flexible, or will becoming flexible make exercise more effective?

Do both.

One of the nice things about being a beginner at exercise is that you can do lots of things at once. So while advanced exercisers have to choose between muscle gain and fat loss, beginners can do both at once.

Do lots of strength and cardio exercise, to build muscle and burn fat, and afterwards as part of your cool down do some serious stretching to improve your flexibility.

You should exercise and than stretch afterwards. Exercising will help you lose body fat and stretching will help you restore muscle after exercise and improve your flixibility