Hmm- really depends. When you're starting out, I'd find a cheap brand with a wide range of wrappers and try a few until you find a style you like.
Personally, I'm a fan of Romeo y Julieta, CAO, and Gurkha.
As far as drink pairings go, easiest way to do it is match the drink color with the wrapper, like
Oscuro -> Sweet dark liqueurs like Kahlua or Irish Cream
Maduro -> Cognac/Scotch/Dark coffees
Connecticut -> Brandy/Bourbon/Light Coffees
Double Claro -> Rums/light liqueurs like schnapps/chai tea