It really depends on the meal; I tend to think of reds as naturally going well with pizza, lasagne, and casseroles with a robust flavour, whereas lighter things such as a cheese omelette might be better complemented by a fresh, crisp white, but it really depends on your personal tastes (as indeed it pretty much does with a non-vegetarian meal).
Reds are generally served at room temperature, while Whites are generally served chilled.
You could pick on the basis of desired temperature if you like.
It’s now a matter of taste, though it’s good to at least follow the advice of a good sommelier once or twice, and then to explore per your taste.
“Red wine with fish. That should’ve tipped me off [to a killer pretending to be a British Secret Intelligence Service agent].” - James Bond, From Russia with Love
White wines can be just as good as reds, but we in the US tend to serve them so cold that their already delicate flavors disappear. A good white can often be served at the same temp as red or just a bit cooler. The only wine I know that needs to be really chilled is sparkling wine. I would be surprised to find anyone who likes that near room temp.