Oh so this is a fun and very layered question. Ancient wining and dining? Why yes I think I will! I'm going to interpret your question a little bit more broadly than the Last Supper itself to give you some context into wine culture and in first century Palestine, since a lot of information on the Last Supper itself is...murky to say the least. I'd prefer to stick with things that are far more clear and less prone to controversy.

So, a quick note before we begin! The economy of the Mediterranean in the early first century AD was incredibly interwoven: since the whole region was controlled by Rome, Roman products quickly spread throughout. Regional specialties were certainly still a thing, but in major metropolitan centres (such as, say, Jerusalem in the 30s), many different vintages and types would be available.

Red and white wines were both in production for most of the Roman period - there's a piece of Greek pottery from the 6th century that specifically depicts the process of maintaining the separation of the marc from the must (how white wines are produced). The whites in production in the ancient world were far cloudier than the ones that we are used to on account of the far more primitive process. Different regions produced very different styles of wine: for example, Africa (the area around Carthage) was well known for a highly valued sweet white wine, while the Western Delta of the Nile was known for a red with a slightly oily texture (which apparently was unnoticeable if properly watered). Different regions followed different practices and traditions to appropriately flavour their wines - and luckily, many of these are laid out in close detail by Pliny, whose writings on the topic are...encyclopedic. They even include a number of methods used today, such as certain soil compositions, different linings for barrels (different resin, different flavour!), among others. Interestingly, one of the most common ingredients that was used in making wine was seawater - the salt (according to modern experiments) was not particularly noticeable (depending on how much was used), and it offered a natural preservative to ensure that the wine did not turn to vinegar. One of the most famous (and popular) wines in the Roman world was the Falernian, described thus:

There is now no wine known that ranks higher than the Falernian; it is the only one, too, among all the wines that takes fire on the application of flame. There are three varieties of it—the rough, the sweet, and the thin. Some persons make the following distinctions: the Caucinum, they say, grows on the summit of this range of hills, the Faustianum on the middle slopes, and the Falernum at the foot: the fact, too, should not be omitted, that none of the grapes that produce these more famous wines have by any means an agreeable flavour.

Luckily, that transitions nicely into alcohol content! Specifically because of the fun note that the ABV of Falernian was ridiculously high: generally, it takes at least 40% ABV to light a drink. Despite this (or, more probably, because of it), wines were always watered down by the more "civilized" folk. Most commonly, it was 3 parts water, 1 part wine - which makes their strength make far more sense in context. Drinking unwatered wine was a very well known way to just get super drunk. If that was your goal, great, but for just a drink with a meal? Watering down was important.

On top of water, though, all sorts of things were commonly added to wine, depending on the occasion. Apicius gives a few recipes, such as this one for spiced wine, which was extremely common for meals:

Into a copper bowl put 6 sextarii of honey and 2 sextarii of wine; heat on a slow fire, constantly stirring the mixture with a whip. At the boiling point add a dash of cold wine, retire from stove and skim. Repeat this twice or three times, let it rest till the next day, and skim again. Then add 4 ounces of crushed pepper, 3 scruples of mastich, a drachm each of nard or laurel leaves and saffron, 5 drachms of roasted date stones crushed and previously soaked in wine to soften them. When this is properly done add 18 sextarii of light wine. To clarify it perfectly, add crushed charcoal twice or as often as necessary which will draw the residue together and carefully strain or filter through the charcoal.

Note: This was a very fancy version for very fancy people. Probably not the kinda thing a construction worker and a few itinerant fishermen would have for themselves. Other additives could include almost anything imaginable, from flower petals to chalk (which apparently was very good at cutting down the bite of the wine in question, but uh). With all other things out of context, this would be the type of wine that would start a meal, though - spiced and flavourful, certainly watered down, and paired with some other sort of finger foods. The people in question at the last supper were pedestrians, but assuming they owned a horse, a couple of glasses of (watered) wine wouldn't mess with them too badly. If it were unwatered Falernian, though...well, think about what it'd be like to down a couple of glasses (not shots) of vodka. And the only ones doing that were looked down as uncivilized and barbarian ;)