Upgrading cheap "cruiser"-type bike for commuting My current bike is this one: http://www.amazon.com/Avalon-26-Mens-Cruiser-Bike/dp/B00BF0DDRG
To disclaim, I don't know very much about bikes, and I'm trying to get more into bikes for commuting and for pleasure. To that end, I suspect that this bike's frame and tire structure are suboptimal for commuting, because there is a shock in the frame, and also two front shocks. As well, the tires are thicker and lower pressure, and what I'm made to understand is that higher pressure is better for commuting, because the rolling friction is lowered.

Basically, what I want to do is piecemeal upgrade this bike, so that in the end I have a nice commuter bike (perhaps with all the fixings), too. My current plans are:


Get new wheels (not in the least because my current ones are not perfectly flat, and I've had to hammer the rim back into shape using a rubber mallet.
I would like a better handlebar, but the angle of the seat stem makes drop bars seem impractical.
Tires more suited to city riding (which go along with the wheels)
Longer term, get a new, lighter frame


For the record, I'm aware that it could be cheaper and would be easier to simply put away some money each month, and then outright buy a nicer bike. However, this is as much a learning exercise as a practical endeavor.

What general trajectory should I take to accomplish this upgrade to commuter bike?

I appreciate any and all advice and/or criticism!
This is what we call a BSO (Bicycle Shaped Object) -- everything on that is as cheap as possible, which makes sinking even modest upgrades into it not really worth it. For upgrading and tweaking, you'd be much better off starting with an old (but decent quality) bike. You'll likely come out monetarily ahead, and have better quality parts to make it easier to learn (e.g. derailleurs which stay in adjustment, etc.). Also, be careful if you're removing dents in a rim with a hammer -- its less safe than the proper tool (and be careful with spoke tension). 

If you want to do something to make it better for commuting, I'd limit it to maybe a set of bar ends if you want more hand positions or a better saddle. You already have slick tires.