I'm in the US too and have never been to a wedding or significant party where we paid for our own drinks - it is customary here to provide the drinks
Me neither. It's the same here, and in Europe
I've been caught out by this a few times.... I have NEVER been to a party, wedding or funeral in France at which the guests have been expected to buy their own drinks..... so I often forget that things are done differently elsewhere.
When doing significant birthdays I provide food, aperitifs, soft drinks, wine, bubbly and hot drinks (tea, coffee). I think for OH's 40th I also did on tap beer.
When attending parties in the UK I need to remember to take money with me and once had to borrow some from my Mum as I was with French friends who didn't understand the concept at all as it wasn't what they are used to - and as they'd paid for flights, a hotel and taxis it seemed "cheap"(IMO) for my brother to expect them to buy their own drinks.
However, thinking it through, there does seem to be a significant cultural and financial difference because "drinks" at parties in France do not involve spirits. And you get 6 glasses out of a 6€ bottle of wine.
In the OP's case at the very least I'd go with a bottle of white and a bottle of red on each table, soft drinks provided and if anyone wants more they can get it from the bar.... so no one is actually forced to buy a drink if they don't expect to - but you are not paying for loads of people to get rat-arsed at your expense.
I was at an event recently where some guests fancied a classier bottle of wine than the host had provided so they got that from the barthemselves and paid for it - seems logical, but I would expect you to provide something for your guests to drink.