To get you up to speed quickly, I will point you to my newbie guide
and once you are familiar with your cockpit, head over to Sim's How-To
guide on using weapons.
As per #1 on my guide, you can use your Steam key to activate the game even if you downloaded the game from ED. I would suggest a FULL INSTALL instead of patching, and I would recommend torrenting the files simply to ensure a "correct" download.
You have a nice set of hardware there, should be no problem to run the game with great eye candy. As to your X52, check out page 38 of the Quick Start Guide (see #2 on my guide) found in the Docs folder in your A10 install directory. That is what is mapped to the real HOTAS, that is what you want mapped on your X52. I would suggest printing it out as well as it shows the default keyboard keys for the relevant commands. That is important because most "help" you will get from here is worded that way. We will constantly talk about TMS Up Short, TMS Up Long, China Hat Forward Long, etc. etc. BTW, "long" is simply a long press of the button/key, about 2 sec, while "short" is a short press, about your normal push-and-release of 0.5 sec.
As for "getting started in multiplayer," there really is no requirement. Or rather, it is up to you and the guys you are flying with. A few of us here in SimHQ are willing to teach new pilots the ropes, so the minimum requirement is having your profile set up properly (or having the print out in front of you!) and a quick read through my guide so you at least know where things are in the cockpit.
Welcome to DCS A10!