I always do that!
I will be searching around random cosplays and see something that i like and be "OMG! I LOVE THAT COSTUME!" and have no clue what it is from, so I go look up the anime watch one or two episodes of it (I'll watch more if i like it) and cosplay from it...
On the other hand, if I don't like the character that has a cool design, i won't want to cosplay them. To me, cosplay is not only the costume but being in charcter too, so if I don't like the character why cosplay as them?
With the last question, if I don't like a charcter's costume it won't turn me from it, as long as I like that anime, i just ignore the bed character designs..