personally i recommend doing both at the same time... that is building and toning. If you want to build fast you can train a different muscle everyday eg: biceps triceps... then quads hamstrings.. then lats abs and then start on your biceps and triceps the next day because they would have recovered by then. Make sure you can do around 8 - 12 reps only with weights, no more no less, and use slow repetitions with good form.
Before you do each weights workout go for a 30 minute run. To lose fat and tone up thers no better thing than jogging and its very easy to improve quickly, don't be discouraged if you feel unfit the first time.
With diet, i take whey protein powder mixed with water AFTER every muscle workout. If you do use protein concentrates its important to look for whey, its the hardest protein for the body to store as fat. If you don't want to get on the protein shakes eat protein rich foods like tuna, steak, chicken, spinach, egg whites and even cheese sometimes.
If you need help to find some good muscle building exercises without machines go no further than this guy
http://www.youtube.com/user/scooby1961.. he's kinda weird but he knows his stuff.