Usually I like to train 'mons that are useful at every step in-game, from lv. 5 to lv.100. I already had bad surprises with Pokemon with funny or cute design and that are good in early-game and that become crap once they get lv.30 and they teammates evolve, such as Watchog or Mightyena; while some other Pokemon that are creepy in early game become very good, such as Breloom or Ludicolo. When bad surprises, bad 'mons are boxed and replaced. When 'mon won't be able to train itself in his early levels, I wait for it to appear in higher levels (i.e Magikarp, Ralts, Cocoon 'mons, Abra, Lotad), so they can at least DO SOMETHING BY THEMSELVES!
I've never decided to use OU Pokemon with strong typing and good Base-stats, such as Dragons, because I don't really like :
1/ their designs
2/ the way they are glorified and mystical in every game (i.e Peter, Clair, ...).
But I won't say they're lame cause I would be like, totally wrong.
I remember having used Beedrill and Parasect (though I think they are usually defined as "not good") in Red/Blue, and they gave me good results. But Beedrill is GSC has become much less useful.
For EV training I must admit I find it way 2 complicated in early-game 'til the E4 (in Emerald) : no information provided (you must establish an EV-counting by yourself), no possibility to reduce EV with Emerald magical berries since they are HELL scarce... And when my team has raised levels and it's ready to battle E4, it's just a pain think : "oh my, they are not EV trained, better go breed new ones that I will EV train and thus spoil an entire game giving exp to useless 'mons". So... Sometimes I try, sometimes I find ways to keep my 'mons and EV train them (Pokemon Glazed hack has GOOD features to allow that : magical berries for pk$20, EV training center,...)
Finally, I also have a big issue with these games : some Pokemon are good in competitive battling but are unable to have interest in-game (terrible grinding ability on wild 'mons, not OHKOing some trainers while game-rushing, not gaining Exp. fast enough as their teammates do). These ones are mainly Stallers or Pokemon that learn Explode and Selfdestruct, and I don't even want to catch'em : for instance Weezing, Forretress, Dusknoir... Saying that I had Dusknoir in Pokemon Flora Sky and it was not EV-trained and totally useless since he was not able to kill any 'mon, nor to resist and stall as he can do in competitive battling with correct EV and nature.