Simple answer is one single club will do little to actually vastly improve your game. Yes a driver will give more distance (so I would personally opt for a good 3W which would give more options).
1 Wedge alone will not change enough - you would need 2 wedges to really see a marked improvement.
Yes a putter would help, but the starters is not too bad if you can get the ball closer (via 2 wedges).
Basically this game is addictive, and IMHO is worth spending money on, as the better the clubs you will possibly get more enjoyment.
But once you buy one club, I would be surprised if thats the only purchase you would make.