My favorites are often the ones I've read most, so when it comes to the Weasleys, I'd say definitely Charlie, (and I ship him with about anyone) followed closely by Ron, then Bill, the twins, Ginny (i like her in femslash pairings), Percy... in next gen, I love Hugo, sadly not written enough. ;)

Then of course I love Harry and Draco and Harry/Draco, not necessarily exclusively. I can read Draco with almost anyone, but not Harry. I love Harry and Ron but as friends only!

and you already know my love for the next gen characters. I think it comes from the fact that many of the fics I read when I first got into the HP fandom were next gen fics. I saw them on my flist all the time, they were written quite often, there were more fests with those characters too.