Prohecies, Factions and Nightfall are stand-alone campaigns that can be played independant from each other. Eye of the North is an expension that requires you to own any of the campaigns.
You can take your characters to other campaigns (and eye of the north) and pick up the story there (not from the very start... but you will be introduced into the story in a natural manner as a foreign hero comming to aid a different continent in trouble).
I suggest you play prophecies first. It has a great learning curve. It is long and slow pased, but the story is kickass^^
Many people will disagree, but I like Factions alot as well. Its learning curve is much steeper, so I don't suggest starting there. The story is short and fast pased, but story is just right for the length of this campaign. The different sceneries are also very nice.
Nightfall I find the least appealing. It's personal preference, but the story is not well written enough for the length of the game, and the sceneries are all kinda monotonous for me (I don't really like desert settings, I guess ><).
Eye of the North is fun new content if you play through it once, but other than that I hope it's not a taste of what's to come in GW2. It's only an expension, so I'll cut anet some slack.
I value things like scenery/story/atmosphere in games, and Guild Wars hasn't dissapointed me. I have played through all campaigns multiple times and still enjoy them. So you are in for a good time, wherever you decide to start your adventure.
Have fun^^
Edit: And yeah, it's very solo-able with heroes or henchmen (It's what I usually do, though I do seek company from a guildie from time to time). As has been said, heroes are only good after you get some skills unlocked (prophesies has quite alot of skill quests that give you free skills

), so it's best to start with henchmen.