It just depends on what you like and what you have access to. Chile is a place to look for relatively inexpensive and good red wines, either cab or carmenere varietals. Santa Rita and Escudo Rojo are two good ones. Assuming you don't want something too tannic, like if you're having a light meal or lamb, you could look for a good Shiraz. I had a really good South African Shiraz for Pascha, it was about $15 a bottle which might be somewhat above what you want to pay. Salice Salentino, made from the Negro Amaro grape, is another good red. It also saves well. One I had this week, which was good but not great, was Pillar Box Red. It's a cab/merlot/shiraz blend. It was about $8 a bottle.
I'm not a huge fan of whites, but I think Chenin Blanc's tend to be good choices. Usually well balanced, not too sweet or dry, and they don't have the grody oakiness that a lot of the more popular whites seem to display.