Ral-clan, I feel like you've had a lot of info thrown at you, much of it conflicting. I wanted to just summarize a few things for you based on my years of using Linux as my primary OS.
**Distros**Everybody has their favorite, and no doubt you've heard countless recommendations. My suggestion is to stick with the Ubuntu family when starting out. It's the best supported, and help is easy to find. Mint is not a bad option either, since it is based on Ubuntu and is compatible with all of the same software. If you want to do more exploring later, there are a crap ton of distros out there.
The Ubuntu family of OS's all run from the same software repository (where your programs are pulled from when you install them from the software center), and can run all of the same software. The main difference is the desktop environment that is used. Here is a rundown of the different Ubuntu flavors:
1.
Ubuntu: Uses the Unity desktop. This desktop is modern with an eye toward convergence (works well on netbooks, as well as full-blown desktop systems. Might be a bit sluggish on older PCs, especially those with older graphics cards and single-core CPUs. This is probably the most polished out-of-the-box Linux experience of all the Ubuntu variants, and the version I always recommend as a starting point if a person's computer is modern enough for it to run crisply.
2.
Kubuntu: Uses the KDE desktop. This is my preferred desktop environment, because it is super-configurable, and the desktop default tools (file manager, text editor, etc.) are the best in their class, IMO. KDE uses up a fair amount of RAM, and while it can be sluggish on older PCs, is quite configurable in its system usage.
3.
Xubuntu: Uses the XFCE desktop. This is my preferred desktop for older PCs. It uses more RAM than Lubuntu, but otherwise is much more fully-featured and easily configurable. The applications run quite speedy on a system like what you are using. LXDE's control panel and file manager, etc. are all quite good. On systems with slow graphics cards, turning off "compositing" (which is what draws shadows and transparency effects) will give you a nice performance boost. I'm really surprised that nobody has mentioned Xubuntu as an option for you, as I think it would be a more ideal balance of features/resource consumption for your particular PC.
4.
Lubuntu: This is the lightest-weight Ubuntu variant. Personally, I miss a lot of the features and ease of configurability of other desktops, particularly XFCE and KDE. With Lubuntu, certain things aren't as easily changed without editing config files, etc, whereas XFCE has more point-and click configuration options. That being said, none of the other options will be more spry than Lubuntu.
Another note: Only Ubuntu and Xubuntu feature the official "Ubuntu Software Center" application. The other flavors have their own "software center" apps, which don't seem to handle getting paid applications as well. You can install the official "Ubuntu Software Center" on the other desktop environments, but you may run into issues with this (screenshots not showing up, etc.).
My personal recommendation for your setup would be Xubuntu.
**LTS vs. 6-month releases**If you prefer stability, you're probably best off only installing/upgrading to LTS (long-term support) versions of the Ubuntu OS's. If you prefer to live on the "bleeding edge" and always have the latest software and tools, then you may prefer to use the 6-month releases. The next LTS will be coming out this month. After you upgrade from your current version to this month's release, you have the option of leaving that install in place and not upgrading until the next LTS is released in two years, or upgrading every six months to the latest version. In my experience, sticking with the LTS is the best option, because although upgrades usually go smoothly, things can go wrong or break during an upgrade, and by sticking with the LTS, you are giving yourself better odds that something won't get hosed. What do I mean by "hosed"? Well, most commonly: driver issues, especially for proprietary hardware, meaning research into why my wireless is no longer working, for example. Not trying to scare you, but it can happen, and it's less likely to happen with the LTS releases.
If you are intrigued by the greater stability of LTS releases, but want to stay with the very latest updates of certain programs (beyond the security updates that Ubuntu officially creates), it is easy to find and add PPA's, which are additional software repositories, usually created for people who want to keep up with the latest developments in a particular piece of software.
All in all, enjoy the experience of exploring something new. Expect there to be a lot to learn. Don't expect everything to go perfectly, and remember: All OS's suck. They all have their strengths, weaknesses, and unique ways of making you want to put a hole through your wall

What is going to be best for you comes down to which battles you're willing to fight. When a Linux system is running well, it will be the smoothest sailing you'll ever know, if your experience is anything like mine. I've also had my fair share of problems over the years, but in every case, I have learned something that has empowered me, and at this point, I am never worried about ending up in a situation that I can't get out of.