First you should decide whether the wine you want is red or white. Find out which one they prefer.
If white, decide whether you want still or sparkling. Sparkling is good for opening in a special occasion like New Year. As some people said, spend €20 on a bottle of prosecco (sparkling white) and you are unlikely to go wrong.
In whites, if you are unsure what to go for, a New Zealand Savignon Blanc is probably a safe bet. Spend €15.
In reds, a €15 Italian red is probably going to be quite good. Elat recommends a Chianti. I would go for a Montepulciano. Either way, A mid-price Italian is always a good bet.
Buy in Lidl, Superquinn or O'Briens. Tesco's selection is not great at the moment and I'm not a fan of Dunnes (especially their reds) lately either.
I'm told SuperValu are good to shop in but I haven't been in one in a while.