Let's see if I can help a bit:
In the PC world, hardware and software are compiled by many different companies (largely led by Microsoft), and the end product is essentially created by plugging these various pieces of hardware and software together. My impression is that Macs do not work quite like this. The way I understand it, Apple creates the hardware and the software for a Mac. Is this correct?
Only partially; with Windows Microsoft creates the OS and a number of major applications for it (Office, WMP, etc), but they don't have anything to do with the computer hardware that runs the OS. They do produce some peripherals (mice, keyboards, the Zune, for example), but so do many other companies.
In comparison, on the Mac, Apple also makes the OS and several major applications for it (iLife, for example), but Apple is also the only computer hardware manufacturer--the only computers that (legitimately) run OSX are built by Apple. On the negative side, this reduces your choice and generally makes the hardware a little more expensive (or, more accurately, doesn't give you the option of buying a budget PC; if you're comparing A to A hardware, Apple's stuff isn't any more expensive); on the positive side, it means that Apple knows pretty much exactly what's going on with the hardware OSX runs on, so there are never any issues with downloading appropriate drivers for your motherboard chipset or that kind of thing.
As for peripherals and additional applications, there is a somewhat smaller selection of things that are compatible with a Mac, but there's still PLENTY to choose from--there are hundreds, if not thousands, of hardware products that are Mac compatible (ALL monitors, ALL hard drives, most mice and keyboards, most printers, most scanners, pretty much all cameras, etc). Not EVERYTHING is, but still plenty to choose from. Likewise there are thousands of applications that run natively on the Mac--some Mac only, some that also have a Windows version. Check a site like VersionTracker.com for examples.
I have been told that Macs are not as easy to upgrade as most PCs. Is this true?
Yes, but it depends on what PC you're talking about--there are PCs that aren't very easy to upgrade, too. The most common upgrades, fortunately (larger hard drives, more RAM) are just as easy except with the Mini, which is hard to get into.
The generic perception among non-techs like myself is that: PCs are better for math and business applications, Macs are better for artistic stuff. Im sure this is a huge generalization, but could anyone comment on the truth of this statement?
Personally, for *most* cases, I think that's a misconception. The exception is Quickbooks and friends and some of the high-end tax software; there's a version of Quickbooks that runs on Macs as well as a few competitors, and some tax packages that do as well, but the selection is somewhat more limited. Most of the big business back-end packages also don't run natively.
As for "math," not so sure about that; most of the major mathematics and statistics packages I'm aware of run on both Windows and OSX, so I don't think there's much difference. SolidWorks and a couple of the other major CAD apps like that don't run natively, but VectorWorks does, and there are a couple of others.
Unless you're looking to run very specialized business applications, I don't think it's likely to be an issue--for most "everyday" stuff there's no big difference. If you meant that the *hardware* was better for one or the other, no. The only difference is most Macs come with somewhat more AV stuff built in than a budget PC--otherwise, the hardware is essentially identical.
Ive also heard that because PC has a substantially larger market share, there is simply a larger selection of software available for the PC world. Is this true?
Yes. But in most cases, it doesn't matter. The thing is, if I'm looking for, say, a video compression application, there are more of them available on Windows than for OSX. But OSX has several good ones, so it doesn't really matter--there are apps that do what I need, so it doesn't matter if the selection is slightly smaller.
Same with, say, video editing. Yes, there are more available for Windows. But frankly, iMovie does just about everything most people want, and does it better, and if that's not enough there's Final Cut Express or Pro, so most Mac users don't care.
Further, depending on who you ask, the shareware and freeware available for OSX tends to have a higher standard for ease of use and attractiveness, so I think in many cases (of course not all) OSX has better options available, even if there are fewer in number.
