Contrary to common belief, you can cut down fat and gain strength at the same time. Diet is most important, and if you don't want to "get huge" and haven't done any strength training before, I would indeed recommend some 5x5 sets of squats, pulldowns and pushups twice a week, but with a comfortable intensity. By that I mean that you shouldn't go to muscle failure, but adjust intensity so that you feel that although you're lifting heavy, you could have lifted a bit more. If you want to do 5x5 with maximum intensity, I would recommend that you do that only once a week. However, IMO this approach is most appropriate for people who want to get huge.
BTW: My secret weapon for the cutting down fat part is coconut oil ... it may sound incredible, but replacing butter with coconut oil can do wonders for your weight loss - and general health. It's because of the medium chain fatty acids that only coconut oil contains in large amounts (more than 60%).