While MvM is free to play, to get the rare robot items(they are cosmetic only) you will need a Tour of Ticket(just you) or Squad Surplus Voucher(whole team) to play Mann Up Mode. They are $0.99 and $1.99 respectively.
Reading the FAQ this is the inforamtion I found the most interesting:
Q: What is a Tour of Duty?
A Tour of Duty is a collection of Missions that may span multiple maps. Tours of Duty only exist in Mann Up Mode. Mann vs. Machine is shipping with one Tour of Duty. We’ll be releasing more Tours of Duty in the future.
Q: What is Mann Up Mode?
When you play Mann vs. Machine on an official Mann Co. server, this is called Mann Up Mode. Mann Up Mode allows you to earn special item rewards and track your progress through various Missions. To enter Mann Up Mode, you must possess a Tour of Duty Ticket.
Q: What is a Tour of Duty Badge?
A Tour of Duty Badge (ToDB) tracks your progress through a Tour of Duty. It will be automatically granted to you the first time you successfully complete a Mission in a Tour of Duty while in Mann Up Mode. Each successful Mission will be marked as completed on your ToDB. When you complete an entire ToDB, you'll receive a random rare item reward and an upgraded ToDB of a higher rank, allowing you to complete each Mission again to earn more items.
Q: What if more than one person on my team uses a Squad Surplus Voucher?
Everyone on your team will receive an ADDITIONAL item for each Voucher used. For example, if all six players in a Mission use a Voucher, everyone will receive six extra items upon completing the Mission. If only one person uses a Voucher, then everyone will receive one extra item upon completing the Mission. If the Mission is NOT completed, no Vouchers will be consumed, and no items will be granted.
Q: Are my Tickets or Vouchers consumed even if we lose the game or are disconnected?
No. Tour of Duty Tickets and Squad Surplus Vouchers are ONLY consumed upon successful completion of a Mission. If you do not beat the Mission for any reason, then your Tickets and Vouchers will not be consumed and can be used again later.
Q: What if I complete a Mission that I have already completed on my Tour of Duty Badge?
In this case, your Tour of Duty Ticket will not be consumed, and your ToDB progress will not be updated. Squad Surplus Vouchers, however, will always be redeemed for items when a Mission is completed successfully.
Bolding is mine. What I find interesting is that tickets and vouchers are only used up if you finish and win a mission. A good amount of other games would require you to buy the ticket again if you lose.