But what will my phone be running when I root it? If I want plain old 2.1 running on my phone, will it be the Google-written version, or a file that one of you genius developers out there created that just looks like 2.1?
If you just root it, your phone will still be running the same 2.1 that is currently on it - it's just you have access to everything now. One way to think of it is that currently you're using a PC running Windows under a general user account. You can still use the phone for most purposes, install third-party apps, browse parts of the file system (in Windows, stuff in Documents; in the phone, your SD card) and even install themes (phone: LauncherPro or ADW). However, you are still locked out of some areas of the deeper-down files.
BUT once you root it, you are now the admin (in Linux/Android, called root), and have complete access to everything, like the stuff in system32. You can now tweak the lower-level stuff. Some apps on the phone like Wifi Tether and Titanium Backup require this access. It is worth noting that just like being a Windows Admin, being the root user does take a bit more responsibility. You wouldn't go into system32 and start randomly deleting/editing files, same with root. Although nothing stopping ya from taking a look around and figuring out what specific files do!
Also, if you need specific instructions on how to change the launcher (or as you called it, the overlay) and/or remove bloat, please feel free to ask. The apps LauncherPro and ADW (they do the same thing, and are free, so might as well try them both to see what you like) change the launcher's looks, without needing root. LauncherPro (and maybe ADW, I don't know) can even hide any apps - it doesn't remove them at all, just hides them in the Application list.
And if it is the latter, are these files the same thing as these ROMs that I'm reading about?
ROMs are a bit different, although they require root access to install them. They are basically an entire operating system for your phone. Just like there're four billion different flavors of Linux out there, there tends to be a lot of ROMs out for a phone. You can test them out and see what you like best. Although I think there's only a couple out for the Fascinate so far.
If I've missed something, or you have more questions, please feel free to ask!