If the storyline is of interest to you, I would do them in order, Prophecies -> Factions -> Nightfall -> EotN
I didn't do them in order (I started Prophecies, got stuck on Ascension Missions, finished EotN, finished Prophecies, finished Nightfall, now working on Factions,) and while it hasn't been a huge deal, it kind of stole the thunder of the story because things that had already been casually revealed by later games were supposed to be surprises in earlier games. Also, while each campaign is separate, there is to some degree an ongoing story in the three main campaigns, which makes more sense in chronological order.
If you don't care about that, here are my other thoughts:
I've started characters in all three campaigns, but only stayed with my first one, my Ranger from Prophecies. She's the one I've been doing all the campaigns with.
Prophecies was, for me, the easiest to get into. It was always fairly clear what to do next and what came next in the story. The main story started in from the beginning, rather than popping up later on. Challenges were scaled well for starting characters. There's little to no "reach the next level before you're allowed to do this," and very little of the doing tasks just to level thing. Leveling felt more natural to me in Prophecies than the other campaigns-- it just happened through normal play, rather than me going out of my way to make it happen.
Post-Searing Ascalon is only the starting point for Prophecies, not the setting for the whole game; there are actually six additional zones that are very diverse, including snowy mountains and jungle. So don't judge the whole thing by what you see right after the Searing, because Prophecies has probably the most varied landscapes. It also has the most complex story with the most twists.
You level up fast in Factions. Very, very fast. I enjoyed the starting areas well enough, but they don't really stick in my mind. I don't really have negative thoughts of them, but not excessively positive ones either. It just wasn't as memorable for me as the starting areas of Prophecies. Once I brought in my Prophecies character, I found Factions much more gripping, but it was fine either way. I wouldn't recommend strongly for it, but I have no real reason to recommend against it aside from plot chronology.
Nightfall had great looking characters and lovely setting. In terms of aesthetics and beauty alone, far and away my favourite campaign. Unfortunately, when I started a character there, I found it really really hard to get into the story, because the main plot is incredibly slow getting started. For lower level characters, there's an awful lot of just grinding to a higher level by killing monsters so something can actually happen.
I ended up getting totally bored with it and putting aside that character. When I brought over my Prophecies character at level 20, I actually really enjoyed Nightfall and found the pace good-- it just wasn't for me at lower levels. So based on my own experience, it wouldn't be my recommendation for starting a multi-campaign character.
Also, bear in mind that if you like the looks from a certain campaign, you can always create the character in one campaign and do the quests to move them to another. Good luck.