With any free-roll like this, you should shoot for the moon. If they allow parlays, then parlay bet as much as they allow under this promotion and parlay enough events to get up to whatever their maximum payout is, which in Las Vegas is typically around $100,000.
If you have to bet on a single event, then find the biggest long-shot you can.
As an example of why this strategy is best, consider the same promotion in double-zero roulette with a $100 bet. If you make an even-money bet, then the expected amount you'll get back is (18/38)×$200 + (20/38)×$100 = $147.37. However, if you bet on a single number, then you can expect to get back (1/38)×$3600 + (37/38)×$100 = $192.11.