I'm ok with a team thing, prize or not.
Only thing is, things like "most weight lost" either absolute lbs or % kinda go against what we preach around the site here as safe and effective weight loss. For example, I'm only shooting for losing 10lbs a month, and 12-14lbs lost max a month to stay at or under 1% of my weight lost per week. I'm unlikely to be motivated to try to lose more than that, even though I'm sure I could.
For "minutes spent working out", how do you define what counts as time working out? I usually spend ~ an hour in the gym 3 days a week, but a lot of that time is resting in between lifts. I count golfing on tuesdays as my workout for the day because I walk the whole time, but it usually takes over 3 hours, and it wouldn't be as effective as 30-60 minuted of focused exercising. I play DDR for an hour a couple nights a week, I would count that. Is that equivalent to the hour I would count if I went with my wife to take the dog for a walk? Someone could spend 2 hours walking a day, and it would be much less effort than a different person spending 1hr a day running. We also know that time working out does not correlate to more progress if your eating at or above maintenance. So I don't really think that time spent working out is indicative of effort or results.
What I think would be nice and consistent with the knowledge base here (but it will take some coordination) is, the team sets a total goal for team weight loss (based on the individual goal of the team members), and the winning team is that which is closest to its goal. I think losing too much for the sake of a challenge should be discouraged. We all preach around here setting realistic and attainable goals. So the best contest would measure how well we succeed at setting realistic goals, and then meeting them.
Example:
Team A sets a goal to lost 100lbs, loses 90lbs, is off by 10%
Team B sets a goal to lose 75lbs, actually loses 85lbs, is over goal by 13.3%
Team A wins the challenge.
Otherwise, if we all do what we should do, the team that weighs the most should be able to lose the most weight in the recommended way in any given time frame.