The food is a buffet, so there won't be a menu. Waiters will come to take drink offers. We have been offered 2 options, and are asking about a third.
1. We can have them offer soft drinks and tea and if anyone wants alcohol the waiter will start them a tab.
2. Or we can have them offer soft drinks and tea and accept the coupons for alcoholic drinks and start a tab for anyone who wants more alcohol than the 2 tickets.
3. We are going to ask if we can have them offer soft drinks and tea and beer and wine, and if anyone wants hard liquor, the waiter will start them a tab.
I mean, we can also offer an entirely open bar, but I am concerned that might be entirely outside our budget.
I think that your intention is to please your guests, but that you are making it unnecessarily complicated. I mean, you aren't considering setting up a ticket system for more expensive food items that aren't on your buffet, are you?
Think of it this way: when hosts give a party in a restaurant or other venue, that venue is an extension of their home. You don't charge guests in your home or give out tickets or offer to run a tab for choices beyond what you have offered, and polite guests don't ask you to do so. But you don't have to throw open the liquor cabinet and pantry, either -- you offer what you want to offer, and as much of it as you want to offer, and the guests politely accept it and don't ask for something else (except I suppose water). It's exactly the same in another venue: you offer whatever you want -- whether it's the full menu or a limited selection or just one choice -- and that's what the guests must be satisfied with.
I would just skip the tickets entirely and have the waiters say, "Would you like beer, red or white wine, or a soft drink [or just soft drinks if that is your choice]?" If your guests want to ask the waiter if they can order a hard drink on their own money, let them do it themselves -- don't have the waiter or anyone else make any suggestion of it if a guest asks if they can have a cocktail. I've seen that happen, and it looked bad -- like the guest was suddenly transformed from a guest of a private party to a potential customer of the venue. Much better for the server just to say, "I'm sorry, we're not offering hard liquor tonight, just [repeat choices]" to anyone who didn't already get that very obvious message from the first thing the server said. If the guest brings up the possibility of paying for it themselves, which they shouldn't, at least it isn't you or your "agent" doing it. If you really want to offer hard liquor but don't want to let it get out of hand, perhaps tell the venue to make it available only for the first 45 minutes or something.
In my opinion, for a guest to ask if they could buy a cocktail instead of accept the beverage choices offered by their hosts would be very rude, just as if the waiter asked them for their choice of three entrees, salmon, chicken, or pasta, and they asked if they could order steak instead if they paid for it themselves. It's just not polite to try to upgrade what the hosts are offering, even if you are willing to pay for it. I remember thinking how nice a glass of red wine would have been when my DIL's father hosted a supper, with soft drinks only, at an Italian restaurant a few days before the wedding -- but I wouldn't have dreamed of ordering one, because it would have been insulting his hospitality.
If the guests just can't be happy without a cocktail, and there is a public bar elsewhere on the premises, they can slip out for a quick snort, the same as if they bought themselves a candy bar or a bag of chips from a vending machine or convenience store in the lobby if they didn't like the food offered -- provided that they aren't away from the party more than just a few minutes, which would itself be rude (just as it is when people sneak out of a reception to watch The Big Game on a TV in the bar or lobby and stay longer than a quick peek for a minute or two "on your way back from the rest room," ahem. Not that I have ever done this myself when the Red Sox were in the playoffs. Well, maybe.) Perhaps a good standard unit would be the time it takes a smoker to go outside for a cigarette? This should be another string ....
Bottom line: offer what you are comfortable offering, and then let it go at that, without resorting to ticket systems or offers of running a tab. If the guests want more than that, it's their problem either to do without or find a polite way of getting it.