Hey now, I do NOT rebuild the fuel pumps, and the only diesel VW I own now isn't even 15 years old. Damn things are way too complex and have way too many adjustments to go wrong. I send that crap off to a shop in Portland, OR.
Anyway, I mentioned a velomobile due to it being the vehicle best suited to the workload you're using, but it's most likely not the best suited to your finances, and I did say that it's not good as a first bike. It's something to consider in the future, basically.
I'll go ahead and drop a link to the late Sheldon Brown's website: http://www.sheldonbrown.com/
There's an absolute treasure trove of information about cycling that he, his wife, and a friend of his have compiled over many, many years cycling and working on bicycles. I'd look there first, long before looking at Wikipedia, if you've got a question about how things work.
Another thing is that in the cycling community, everyone has a different opinion. Sometimes this is due to different experiences, sometimes this is due to different desires. For instance, ever since aluminum frames came out, there have been debates over what material a frame should be made out of (a high-quality steel frame has a springiness to it that can feel quite nice to ride, and the tubing tends to be much thinner than other frame materials, so some prefer steel for aesthetic reasons as well). And there's also carbon fiber and titanium, but that just gets really expensive, and isn't called for for a commuter bike. Honestly, for your first bike, either steel or aluminum would be fine. (If you do get a steel bike, ideally get a chromoly steel frame, "hi-ten" steel is the cheap, heavier stuff that doesn't have anywhere near the supple characteristics that chromoly steel is known for. That said, my smoothest riding bike is a cheap single-speed Dahon folder made of hi-ten steel, the trick being that it has a sprung saddle.)
As far as a "Newegg for cycles", things tend to be more scattered. In the cycling community, there's a strong push to use your local bike shop instead, even if it's a little more expensive, because many local bike shops are excellent small businesses that take the time to help you. Sounds like your local bike shop is NOT one of those excellent businesses, though, so the main online places for bicycles and parts are Performance Bike
(which also has brick and mortar stores), Bike Nashbar
(also owned by Performance), and Bikes Direct
. None of those places cover recumbents or velomobiles at all, but those are very much niche market. That said, as a newbie, I would HIGHLY recommend that you actually go to stores and try bikes out (and, please don't waste a salesperson's time by "showrooming" - if you like what you see and they've spent time helping you, buy it - but at the same time, if they don't have anything that works for you, that's also understandable), see what fits you and what you like. I wouldn't order a bike sight-unseen unless I knew exactly what I wanted, and knew that the bike was exactly what I wanted.
Most bikes you'll find are going to be equipped with derailleur gearing nowadays, for what it's worth, but internal gearing is becoming more popular for things like commuter bikes (where they're ideally suited). You will want a rack and fenders (even if you're not riding in the rain, you may want to go for a ride when the roads are wet). You will also want good lighting, even if you don't plan on riding at night (sadly, a lot of front lighting sold in the US is mediocre).
Most low-end bikes that are sold in the US use some form of rim braking, which is OK, but not my favorite. Drum brakes aren't that popular, but can be excellent for a commuter bike (although I've not used them - I wanted to retrofit a front drum brake to my folding bike, but the fork is too narrow for any of the readily available drum brakes), and disc brakes are fairly popular and are extremely effective (but can be a bit tricky to adjust, depending on model). Coaster brakes are not usually a good idea for various reasons (you can't backpedal to rotate the pedals to where you want them, for one).
Oh, and regarding types of bicycle... as far as upright bicycles (which is pretty much everything that'll be inexpensive), it basically depends on how upright you want to be - some bicycles have a very upright riding position that's similar to a cruiser motorcycle (crank-forward bicycles), but those tend to be very unaerodynamic, some are like a standard motorcycle (the hybrids (which are a hybrid of a rigid (no suspension) mountain bike, and some road components (mainly tires)) being the biggest example, and some commuter bikes use hybrid geometry), some are like a sport touring motorcycle (many touring bikes, and many commuter bikes use a touring geometry because touring and commuting actually have very similar needs, just with less cargo), and some are like a sportbike (road bikes).