There is still RP on GL, we just *coughs* don't check our own forums often enough...
ICQ, Vent and alliance chat are the main methods of communication these days, which means things can unfortunately be a bit opaque to new people.
You can find people every Tuesday at the EM event, which almost always start in Britain - either at the EM Hall (which is the northern Counselor's Hall, directly SW of Castle Blackthorn) or at the Warrior's Guild directly south of Castle Britannia. These events are designed to appeal to a mass audience and sadly not everyone there RPs.
You can also find pure RP every other Monday night at the High Council of Britannia in Compassion Grove. It is a good way of learning what's going on in the realm and meeting a good number of players. Since its a meeting, it can be a tad dry, however.
I'd suggest stopping by the Nameless Rune Library directly south of the Yew moongate (the western building in the side-by-side Library Complex) and perusing the runes in the white armoire on the first floor - look for the Jerred Ghyss Civic Center (this is where the High Council meets.)
There are other scheduled events as well, all of which can be found on the calendar, available from the main GL page -
http://gl.uorpc.net
As far as "factions" go, things aren't what they used to be. All the good guilds are allied (called the Britannian Armed Forces, or BAF) and essentially function as a metaguild, though the individual guilds still have their own focus and leader(s).
There are evil guilds as well, and they are allied, but they tend to have drastically different motivations and aren't particularly apt to assist each other in the long run. They are warred to the BAF, so there are opportunities for RPvP, though that is by no means mandatory. (It is also strictly governed by an RoE)
Which would be best for you really depends on your personal tastes.