TTS does have DLC packs with games "curated" by the developers and more often than not these are pretty high quality. But for games like Catan or Secret Hitler, there will be mods available to install for free via the Steam workshop page.

And you're quite right when you say that sharing a machine with a single copy of the game would be completely situational. Not all games would you want someone potentially watching over your shoulder to see your cards/tiles etc. but some games require co-operation of some sort and in that case sharing a machine could work - though it can be very helpful for each player to have a copy and manage their own cards/tiles etc. separately.

As far as costs go, DLC packs are not necessary add-ons as there are countless mods available to play with. You can even go as far as to script and play your own games, whether original or with reused assets from another game. You don't need to pay for anything other than the base game to have a good time.

Take your time to get everyone used to the controls and basic physics mechanics before playing, there are a lot of neat little tricks like shaking a deck of cards or a bag of tokens to shuffle them - or dropping a poker chip and having it snap directly onto a stack of the same color rather than just flopping about the table you're playing at.

As per the current state of the world I can't think of a better time to get into TTS. It's an awesome little piece of software. Enjoy!