I see that there are a number of distros you can download directly from your site. What is totally confusing to me are two things. First of all, how do you choose which mirror to use from a lengthy list of them? The much more vexing problem I have is this. AFTER downloading a distro and looking at the extremely large list of files that I have downloaded for the distro, I am totally lost since there are always seems to be about forty or so files listed. I don't have the slightest idea how to continue even before burning the files to a DVD disc. Do I just go ahead and copy literally every files? How do I proceed afterwards, then, to have a working copy of the distro I have burned? I will post some personal info as a hello soon. Think this site is great!!

Welcome!!

Regardless of which site you use, just download ONE FILE for a CD or DVD. Most distros can be installed from one CD, with SW added later. I would always go that way----unless you have a slow connection (in which case it might be better to get a DVD by snail-mail.

You will typically download on file ending in "*.iso". This gets burned to a CD (or DVD) using the option to "burn from image" or similar. Then boot from the CD and follow the instructions.

The only other choice is 32-bit vs 64-bit. Most distros are now available in 64-bit versions. but I would stay with 32 while you are getting your feet wet. (32-bit OS works on both 32 and 64-bit HW)

Ideally, you would choose a mirror that is located geographically closer to you than the others. This isn't absolutely necessary, but it can help your download go a bit faster, and clogs up the internet a little less.

If you download the correct stuff, you should not have "about 40 files or so", but instead, you generally have one or two or three or more .ISO files (these are the CD or DVD images, and can be 650MB or larger) as well as one or more CHECKSUM files, which could be individual text files containing a long string of letters and numbers, or could be a single text file containing several long strings of letters + numbers, one string for each .ISO file downloaded.
Sometimes the checksum does not need to be downloaded as a separate file; instead, it's given right there on the download page.

To use the checksums to verify that your download has not been corrupted along the way, you would use, as an example, a program called "md5summer" for Windows. NOTE: I'm not a Windows user, so I can't give you specifics about using that program, but basically, you "read" your downloaded .ISO file using md5summer, and you will be shown a checksum string of letters+numbers that you COMPARE to the string provided when you downloaded the .ISO. If they match, your download is good

So.. Once you have downloaded all the .ISO files you need, you must burn them to CD or DVD. If you download CD images, it is best to burn them to CD's, not DVD's. a CD image as around 650-700 MB, while a DVD image is several GB usually.
Using Windows in the "old days" I used to use a free program called "Infra Recorder" to burn my first Linux images to disc. It's a really simple tool to use; just choose a slow burning speed, and using its menu options, select "Burn ISO image to disc" and select your .ISO images that you downloaded, and click the GO! button.

Once you have burned your images to CD or DVD, it is wise to again use your "md5summer" program, to verify that the burned media is OK. Chances are, it's OK, but checking this NOW can save you headaches later when weird things are happening. Again, I can't give specifics about using md5summer or other Windows checksumming programs, but another member can probably help us out there.

Remember: You don't just COPY a bunch of files to a disc; you must "burn .ISO image to CD or DVD" for it to work

Best regards, and if you need more help, please just ask away!
Welcome to LQ.

Sasha

As for choosing a mirror, it's usually a good idea to choose one that's close to you. For example, I use UK or mainland European mirrors, because using ones further afield mean I get a lower download rate.