Apart from rake and tournament fees, you don't have to pay any additional costs to host your game online at a mainstream internet poker destination. The rake is a percentage of a cash game pot that the house keeps for itself while a tournament fee is the portion of the buyin that's retained by the room. This is the way that the sites make money, and there's no need to pay anything extra.
Some mobile poker apps follow a different model wherein basic functions are free but there may be a charge for running private games. If you do decide to install a poker app to play amongst your group, always do your research first to see what the costs will be.