Well, I picked up the bike last night and I've ridden it a couple times to get used to it and try to make necessary fit adjustments.
Riding a fixie wasn't quite as strange as I thought it would be, I actually took to it fairly easily.
I'm pretty certain now that the platform pedals simply have to go because I've had to fling my legs out to the side twice in two rides. Granted, I am a n00b and I have a lot to work on as far as form, cadence, and general practice goes, but when going down a slight incline it was really difficult for me to pace my cadence and not get going too fast without my feet being thrown from the pedals.
So, it looks like I'm going the clipless route. I'm heading to a couple bike shops later today to see what they have and maybe try some more shoes on. Is it standard practice to let you try out shoe/cleat/pedal combos before you buy, or do places tend to shun that with the thought that they could no longer sell the product as new if it has been clipped into? Again, I've never used clipless before so I'd really like to be able to compare some of the options that are out there to see if any one of them stand out to me as being inherently easier to get into or out of.
Thanks to all of the replies so far. It gives me warm fuzzies to know that some people are out there and are willing to provide some insight.