Depends VERY much on exactly when and where your prospective tavern was. "Medieval" covers all of Europe over the course of a thousand years. A tavern in 15th century Italy would be a very different proposition from one in 9th century England. Basically, the later in time and the more urban the setting, the more likely that the innkeep would be running the inn as a business exclusively. The earlier and the more rural you are, the more it's just a well-off peasant farmer with a bigger-than-average house taking in guests. It would have been family-run (like a modern bed and breakfast), but a big professional operation might have apprentices or hired hands to help out.
In many settings, what's been said about brewing beer on the premises would be true, but again, the later and more urban you are, the more likely that brewing will have been done as a separate business by professional brewers, and the innkeep will have bought his beer from them to sell in his establishment. Wine, on the other hand, really requires the work of a specialized vintner and can only be made in grape-growing areas. If your inn isn't in France, Italy, southern Germany, etc., it will have to have been imported.
We have no comprehensive guide to medieval prices, and it's unlikely most taverns had a menu and charged people item-by-item. More often you paid your shilling or whatever for the night and got a bed and a share in whatever the kitchen happened to have brewed up that day. Kenneth Hodges has pulled together a lot of the scraps of data we do have on pricing here... http://www.luminarium.org/medlit/medprice.htm . Note that his prices on alcohol are by the gallon, so they probably represent what the brewers and vintners (or wine importers) were charging wholesale, not what you'd actually pay retail at a tavern.
Guests would be anyone with cause to travel - diplomats, pilgrims, students, and merchants above all. On the tavern side, of course, it would be the people of the village or the neighborhood of the city, and the makeup would reflect it. Most would be middle-class and down; noblemen can generally find hospitality with other nobles without lowering themselves to rub elbows with commoners, but surely there would have been the occasional exception.
Other answers are accurate that churches did offer hospitality, but this was quite distinct from the innkeeping business. Church hospitality was supposed to be an act of charity that you wouldn't charge for. However, there certainly WAS an expectation that travelers with means would make donations to churches in thanksgiving, and the hospitality business could thus be a big source of revenue, especially if the church could boast some prestigious relics. "Hospitals" in the medieval sense were refuges for poor and sick travelers, especially pilgrims. They were not so much "hotels" as homeless shelters or something like the lodging side of a modern YMCA. They would offer basic nursing care to the sick, out of which grew the modern concept of a hospital.