As for new aliens: it's more important to have genuinely new concepts for aliens than new designs. This is what always bugged me about the trajectory of the Klingons, which clearly illustrates a few fixed niches in the corpus of Trek aliens: the Klingons were initially avatars of the evils of dictatorship, then were re-designed and pushed into the "warrior culture" niche the Andorians had seemingly been initially conceived for, and then another species with more elaborate make-up -- the Cardassians -- had to be introduced to inhabit the Klingons' old vacated niche.
Good point! Although in the novels and such between TOS and TNG some writers tried to turn the Romulans into that kind of Samurai-esque culture, before the new series began portraying them as a blend of Roman Empire and Soviet Union.
Klingons of course began as (to quote David Gerrold) "Mongol hordes with ray guns and space ships."
Personally I feel the Cardassians were the single best developed alien culture in Trek
, beating out even the Vulcans. On a visceral level I eventually felt I understood Cardassian culture in the same way I have a real sense what Germans, French, Italians and English are like.
I personally would like to see a species -- if we want to stick with the old Trek formula of hanging a species' identity around a simple, vivid hook, which is not realistic but is dramatically understandable -- conceived around a philosophical dedication to comedy. Comedy as inky-dark as the void. (This is a variant on the anarchistic species idea I've batted around before.)
Ever read The Uplift War
by David Brin? Among the (many) alien races explored in that book are the Tymbrimi, who revere humor. To them, the greatest artform is the practical joke--which only achieves greatness if it turns around and catches the original trickster in ways he could not have possibly planned. They say when that happens, it is proof God really exists.