Alright, let's see ...
The main reason is that I feel that I need to at least try it. I have been on E for nearly three years now and have seen many good games come and go that were system-based. I feel like I am missing out on something important by limiting myself due to my lack of understanding.
That's as good an answer as any, I guess, but before we get down to details about maybe playing together, let's be clear about two things: (1) If we start something and you find it's not to your liking, opt out any time you like. Don't feel you need to go on when it's not fun for you. Sometimes players, GMs, and systems just don't mash well and you only discover it some time into the actual game. These things happen. (2) If one system game does not work for you, let it not stop you from trying another one. Keep an open mind and don't base your opinion only on what I say or do. If I introduce you to system gaming it will be only my personal take on it - nothing more.
The main thing I have heard about them is that it is basically like a Freeform game, but major (and some minor) actions such as fighting a foe or talking your way down to a better price requires certain dice rolls that depend on character stats that are also determined by rolls. Characters also level up and increase their stats over time. The Dungeon Master (A DM, which I have mistakenly called a GM until now) controls the world and creates the situations the players find themselves in.
I guess you can say that I expect a fluid world created by the DM where the characters/players adventure that ranges from life-or-death combat to intrigue to simple tasks like trying to get a cat out of a tree. The dice rolls generally range from epic fails (the 1s) to epic wins (20s or whatever the highest roll may be), always providing an interesting result. I really don't know what else to describe in terms of what I expect beyond that extremely simple description...
DM, GM, Storyteller ... potahto, potayto.
All these terms are valid, as long as they describe the same thing. Some systems prefer one term, some another.
But yes, the basic idea is to introduce an element of randomness into the resolution of certain situations (without neglecting a character's skills / aptitudes / whatever, least it turns into a complete lottery of results). There are certainly situations when the dice should not come into play because the task is basic enough that anyone should be able to manage it, and times when a character's abilities should figure into the outcome at least as prominently as a dice roll, to give specialists in a certain field a chance to shine in that field.
A forum-based system game will also not capture quite the same feeling as playing with people around a table and rolling dice in the real world sometimes provides. It's like ... maybe playing poker with some buddies in RL vs. playing online poker on the internet. The game and the rules are still the same, but the feeling is different. It's something to keep in mind when you hear people talk about their experiences with system games: Are they talking forum or RL?
What exactly do you mean? It really depends on the setting. For example, if it's a Steampunk setting, it may start out as a simple journey between towns where a Sheriff, Musician, and Ex-soldier find themselves drawn into some insane plot. It could be a fantasy setting where a couple of unlikely companions find themselves hunted by the so-called 'good guys.' I don't really know how to describe how I imagine it going. :/
What I guess I meant when I asked how you might expect it to go is (for example) how much you expect the dice to come into play, how structured you imagine the game to be, so I guess.... the level of "roll playing" vs. "role playing". (Those two terms you might hear now and then when you hang out with system gamers long enough, but personally I think it's a false dichotomy, as how much roleplaying goes into a game doesn't depend on the rules, but rather the GM and players, but that's perhaps taking the topic too far into gaming philosophy.)
All that said, what I could offer you is a system game using some relatively simple rules (Feng Shui for something modern, Dungeon World for something strictly fantasy, or maybe something homebrewed) but not d20 Modern. While I have a few rulebooks based on d20 Modern, I've never played it and I am not sure if it is the best system for a complete newcomer. It's not at all a bad system, mind you, but it may be a bit too much for an introduction to system gaming.
We could do a One-On-One with me as GM or we could ask for a few more players, once we agree on a basic setup.
But please feel free to take your time thinking about this. I wouldn't want to close this door on you. If you'd like to wait a bit and see if anyone else offers some options that's fine by me.