I would suggest a 7' or 7' 6" for 3 or 4wt line. The 6' 2wt sounds like a great idea, but after going that route for a while, the hassle of having a rod with such limited uses is frustrating when actually on the stream. And no, the fish won't "feel bigger" that's a bunch of crap. You're just going to haul them right in whether you have a 2wt or 4wt rod. If you hook a larger fish its going to put up a better battle that you can appreciate regardless of the rod in your hand.
The longer length of a 7' or 7' 6" rod will help in a lot of situations, for instance if you have to cast over some exposed rocks or logs it will allow you to hold your line up off the obstructions. The length also helps if you are trying to dap or high stick a fly into a tight spot. The heavier line will make casting a bushy or weighted fly easier and thus your fishing will be more fun. Making accurate cast into tight spaces with a bushy dry fly or streamer is a lot of fun. Struggling against a light breeze or with a light line trying to cast a weighted streamer is not.
Certain people are going to chime in and say how they can do all that with really short, and really light rods. Yes, I'm sure they can, I can too. That doesn't mean its enjoyable, and it doesn't mean a short 2wt is a versatile rod, even for brookie fishing.
2wts can be a blast, but conditions have to be just about perfect. That means no significant wind and smaller flies. On the other hand 3 and 4 weights can do it all. Save the 2wt for later, for now, get a serious small stream rod and go for a heavier line weight in my opinion .
Kev