I second Mint.

Linux is a kernel; a distribution is a kernel plus user space tools. Most distributions are mainly configurations tuned for specific use cases - work, gaming, servers, etc. For example, the GUI part of any base OS constitutes over half of the disk space and memory use; if you're running a server to serve web pages, you don't need all that crap.

Unlike Windows or OSX, there are literally dozens of GUIs you can choose from, and most distros focus on setting up one really well as the default.

Note that you can add, and for the large part, remove any Linux on any distro, so you could start with a server distro or a gaming distro and by adding or removing end up with essentially the same system.

The most significant difference between most distros is the package manager, the thing you use to install software and manage dependencies. Honestly, that's not important at this point, but it will be the biggest distinction after you've been using Linux for a while.

So: Mint. It's a desktop/laptop distro, it's designed to be easy to install and use, and you can mostly use it completely without ever havingy to drop to the command line. When my dad, who's approaching 80, bought a laptop last year and didn't want to register with Microsoft or give them his credit card, I walked him through over the phone downloading Mint, burning it to a USB stick, and installing it. Most of his questions were things like finding an image burner, which keyboard/layout to choose (during install), which type of install to chose (HD partitioning); nothing he couldn't have figured out by making guesses and mostly choosing the defaults. Since then, I've received one call about setting up the printer, which turned out too be a printer issue because his son-in-law had changed the WiFi password and not updated the printer (he obviously doesn't use his printer much).

Mint is an excellent first distro. It may not be your last distro, but it's an easy conversion option. You don't have to update the software on it often, it's easy to use - familiar, for Windows folks - and really just an all-around great first choice.

Three things I do recommend:

1. Do not yield to the temptation to dual-boot. This is the single biggest source of problems, mainly b/c Windows likes to dick around with the boot partition and screw up Linux. If you can, just dedicate the machine to Linux.
2. Do not use vfat or NTFS, thinking you can maximize Windows comparability. You can use it on USB sticks, but just don't put it on any of your HD partitions.
3. Do not using the default partitioning, which puts (almost) everything in one big partition. Instead, make separate "root" and "home" partitions. You may need to find a tutorial - it isn't hard, but I can't explain it here. You'll want to leave 500GB for root, if you have it, and everything else for home. Root can be smaller, but no less than 100GB is my recommendation. Choose btrfs for the filesystem for both.

Suggestion 3 gets you two things: first, it makes changing distributions in the future far easier; all you'll do is replace root and you'll keep your home partition - all your personal, user files: music, docs, pictures, etc. Second, btrfs will let you use snapper, which is a tool that takes snapshots of your filesystem. Snapper is similar to Time Machine on OSX; there's even a Time Machine-like GUI tool for browsing and accessing snapshots.

Start with Mint. You can always change later, and if you partition your drive like I suggest, it is pretty easy to switch.