Weight training is a funny beast and you might find different results for your body. However, for me weight training often causes water retention. What does that mean? Well, if I'm weight training quite a bit the results of that might not show up on the scale immediately BUT I lose inches like crazy (and isn't that infinitely more important?
). Now, if you are seriously lifting (as in lifting heavy so that after your second or third set of, oh, 10 or so you feel like you cannot do even one more) then you can also see a temporary increase in your size (again this is due to water retention) but this does go away after a day or two (so don't freak out!).
Cadio is really great for your hurt and endurance. It also burns a lot of calories quickly. HOWEVER, part of weight training is that you tear your muscles, when you rebuild these muscles (that's when you're retaining water) then you continue to burn calories so in the long run weight lifting can help you to burn more calories total. Since you're doing a biggest loser competition, I'm assuming you're familiar with the show. On there they do a lot of both lifting and cardio so clearly something works there.
One reason you get so much conflicting info is that all of our bodies react so different to EVERYTHING. Some people do well on high-carb diets, others only lose with lose carb. Some people love calorie counting, others do amazing with intuitive eating. It's the same with exercise, unfortunately, I can't tell you over the internet what exercise your body will respond best to.
If I were you, I'd do something like 5-10 minute warm up. Then a good 20 minutes of heavy lifting, followed by a 15 minute HIIT workout (assuming you go to the gym ~3x a week). That would be pretty intense but it would help you burn quite a bit of calories. If you have time to go more often why not alternate cardio and weight lifting days? You can lift two days after another so then you'd get a good mix of the two. Also add in a lot of activity into your life by simply moving (take lots of water/bathroom breaks, clean like crazy, take long walks etc).
Honestly, though, you don't have much to lose so the reality of it is that it might be much harder for you to drop the weight than someone else who has a higher starting weight. I'm not saying that to discourage you but just to give you a heads up if the scale isn't moving as quickly as you'd like. The good news is, though, that if you stick with it you WILL see results!