The game runs quite well on dialup, actually. You lag a bit in the major cities since theres so many people, but in the explorable areas and the smaller outposts everything is pretty smooth since its all instanced. A little jump here and there but completely playable. This isnt so much a game about reactions than using your head and using your skills at the right time for the situation. I'm playng a monk/mesmer (well, monk since so far I havent used any mesmer skills), which means Im a healer. When I panic and shit gets out of hand we die. If I stay calm its surprising how well Im able to keep us going.
I'd definitely try it. They offer 10 day/14 hour trials or whatever. Heck, I just got a trial key in Eye of the North if you need one. I believe it lets you try all the expansions too. Just remember, the begining areas are kinda slow to get you used to the game. Later stuff is much much cooler/more challenging. And the Missions (as opposed to quests) are story based with cutscenes and cool moments in them. Definitely try them.
As for which to get...hard to say. Prophecies is fun and seems to contain the main storyline. It kind of has a neat fantasy look with some cool monsters and stuff. Mostly typical classes (ranger, monk, warrior, elementalist (mage) necromancer, mesmer (a odd sort of class). Factions is asian/chinese themed with its cities and player models. You get the base classes from Prophecies, plus 2 new ones (assassin and ritualist). I read it was the weaker of the expansions. Nightfall is african themed, again base classes and 2 new ones (dervish and paragon). This rated very well and would be a good start I suppose. It introduces Heros to go with henchmen. Henchmen fill out our group when you solo or only have a few players. Heros do the same, but they have better AI, you can outfit them with weapons and choose what skills they use. All the campaigns offer new skills to every class.
Those are all stand alone games, you can buy and play any of them. Eventually you can take the character you made in one and travel to the lands of the others. Eye of the North is the only true "expansion". It requires you own one of the first 3 games. It continues the story started in Prophecies, so you might want to play that before you get it. You also need to have a level 20 character to go play the expansion content. I just picked it up today and dont have a level 20, so I cant really comment on whats included.
Just remember, its more about smartly using your skills than your upber level, weapons, and armor. Dont grind to get XP to level because tis not really as important here.