I "team collect" the Oilers... but a very small and specific want:
A RC / GU / Auto / Picture as an Oiler for every player to have played with them. I typically try and do this with the fewest number of cards needed. I also try for "best" (or at least "best I can afford" Rookie Card. I also work in a few other cards here and there... something that's really cool (IMO) but falls outside of those parameters.
So, when trades happen, it doesn't affect my collection a whole lot. Sam Gagner, for example, I'll be keeping my Cup ARP as part of my Oilers collection. I've also got a auto'd Authentic Moments (which I think I bought from you!) that won't be going anywhere. I don't need to add anything else of Gagner (had no interest in it anyway) and I happy to keep what I've got.
Teddy Purcell, I'll be looking to grab a Cup ARP. Nikitin, that the Oilers recently signed, I've already got a Cup Rookie / Auto incoming, and a KHL Jersey card (he's got no NHL GU cards, I don't imagine one will be getting made anytime soon). In the case of both of them - I'll look to add something Oilers related when they become available. Maybe an insert, a GU, an Auto, something that looks nice anyway.
For the draft, I don't really get too hung up on it. For the lower round picks, I may eventually add Heroes & Prospects GU and/or Auto cards. Guys that I don't think will get auto'd NHL cards. For the top picks, I'll just wait for rookie cards to come out. Even then... I usually wait until the end of the season, so I can decide what I think is the "best" one. The Cup is obviously the top one, but I would imagine Yakupov will be out of my price range (like Eberle, Hall, and RNH before him) so I'll find something else.