What kinds of wine are available
In general, Ancient Roman wine was more oxidized, sweeter, and more bitter, compared to ours, although the Romans preferred less bitter. It was fermented naturally, without added yeast, and was probably in the 10-14% ABV range.
Ancient Roman wine was always mixed with water (occasionally sea water), and sometimes herbs/spices (conditum), or honey (mulsum). There were various additives or techniques, like smoke, to impart flavor. Horace suggests that a particular wine might be improved by mixing it with "the sediment collected by the yolks of pigeon eggs" (Satires, II.4.55ff). And wine was noted for changing flavor depending on what it was drunk out of.
There were as many different varieties of wine as there were places in the Mediterranean, because wine varieties were named by location (like contemporary French wine) and not by grape type (pinot noir, etc.). Reds were more common and whites were typically much more expensive. (See vintages link below.)
The most famous was Falernian wine, from the slopes of Mt. Falernus (north-west of Naples), which "existed as both a white and a red, and in two styles, dry and sweet." Falernian gained a kind of legendary status, but by Pliny the Elder's time, it had begun to lose favor, and he reminds us that "each locality has its own period and its own rise and decline of fortune" (XIV.65)
Similar to today, the cheaper wines were made and sold with minimal to no aging, but more expensive wine could be aged 10-30+ years old. Pliny says that he drank 200 year old Falernian wine from the most revered vintage, but that it was "so concentrated as to be barely drinkable."
Who do I buy it from? What kind of container does it come in?
We're talking about Roman citizens here, but there's a big difference between the average citizen under Caracalla in AD 212 and senator in 200 BC.
Anyone of the lower classes (or later stages of Rome when citizenship was more common) would buy wine in taverns or from various street vendors by-the-cup.
Almost everyone rich enough to have a villa would have a vineyard (or twenty) and make their own wine. Wine was big business and Cato, Pliny, Varro, Columella, and many other authors wrote detailed instructions on how to make wine and how to set up a villa. The excavated Villa della Pisanella at Boscoreale was laid out with a storeroom filled with 96 ceramic dolia (each 125–200 gallon / 475–750 L) for wine storage and 5 dolia for olive oil. This is almost exactly the same ratio that Cato suggest (3-4 of olive oil per 100) for a typical villa.
But not all of that wine would be for consumption at your dinner parties. A lot would be sold and I'm sure you'd want to buy some variety.
A wine merchant would be one main place to buy/sell your wine. Wine would be sold in ceramic amphorae (roughly 7 gallon / 26 L). Lucius Eumachius of Pompeii was well known for his wine vineyards, and his wine amphorae have been found as far west as Toulon, France and as far east as Ephesus, Greece. But most wine was consumed locally.
You could also trade wine with your friends or use it as a commodity in trade.
How much does it cost?
I don't know how much a typical amphora of wine would sell for, but we have extant tavern menus and edicts which tell us what the diluted, by-the-cup prices were. It should be noted that Romans almost certainly suffered from Falernian wine fraud, just as we have current-day olive oil fraud, Kobe beef fraud, and fish species fraud.
Diocletian's Edict on Maximum Prices (301 AD) set a maximum price for a sextarius (Italian sextarius ≈ 1.14 pints or 540 mL) of ordinary wine at 8 denarii, which was roughly 1/3 of the daily wages of a farm laborer. This edict also lists the max price for Falernian wine, but by this time, Falernian was far from the height of its desirability AND this was a time of huge inflation, so take them with a grain of salt.
At Pompeii, we can find preserved menus that lists prices for sextarii of wine: "For one as (bronze/copper coin) you can drink wine; for two, you can drink the best; for four, you can drink Falernian."
For soldiers, the poor, and slaves, there were cheaper drinks, like posca, which was something like adulterated 3rd pressing.
Do you know that great line from Homer (Simpson): "To Alcohol! The cause of, and solution to, all of life's problems."
I think I may have stumbled on it's (coincidental) predecessor:
Baths, wine, and lovemaking destroy our bodies,
Yet lovemaking, wine, and baths make life worth living.
(Palatine Anthology 10.112)
Thurmond, David. A Handbook of Food Processing in Classical Rome. 2006.
Boatwright, M. Gargola, D. Talbert, R. The Romans: From Village to Empire. 2004.
Bezeczky, Tamás. Italian Wine in the Eastern Mediterranean. Amphorae from Etruria, Latium, and Campania from the fourth century B.C. to the first century A.D. The Case of the Ephesian Amphorae. 2008. Bollettino di Archeologia Online
Grout, James. Encyclopaedia Romana. Wine and Rome and Roman Vintages. 2018.