I personally don't see a problem with learning multiple classes ICly, except in cases where someone is going to try to pull off being The Best at them all. Specializing/excelling/mastering one and having good, solid understandings of complimentary classes is (in my opinion) perfectly fine.
Moving on to the actual topic, though... Unless you're planning to let the first fifteen or so levels and the Main Scenario have a Big Influence on your character, there's no real reason (that I can think of) that you can't just pick the city you want. CNJ, THM, and ACN are all complimentary classes, you're likely to want to get all three up to at least 15 for cross-classing skills and Job requirements. You can also make a bit of nice money this way, by holding onto the gear you get during your first 1-15 leveling spree, and taking the Allagean coin rewards when you run the other two  classes.
As for which Archon you're dealing with... as far as I've seen, once you get past your Envoy mission it's all sort of moot. You deal with whatever Archon is already paired for the region you're currently questing in (Y'shtola for Limsa regions, Yda and Pap...something-or-other for Gridanian regions, Thancred for Thanalan). There might be slight text variations in cutscenes, but you'd really have to look for them.
Now... if you're wanting those first fifteen levels/Main Scenario stuff to have effect on your character... Gridania/CNJ and Uld'dah/THM are easy. With a bit of luck or with an escort, you can run between Gridania and Ul'dah at level 1. Pick the city you want to do the Main Scenario with, run and get the job you want to use, come back to the city you chose, and then just work it into your story that you periodically need to travel to do your class quests.
Limsa classes and Main Scenario stuff with another city as your starter... the way I see it, it would require some more working that you may or may not be willing to do. Essentially... you'd have to run two characters until past the Envoy quests. Character A being the one you're going to keep, grind that up to where you get your airship pass, move to Limsa, then grind up to fifteen again on ACN. Then make Character B with a similar name and appearance, have them start out as ACN, and then level up through the Envoy quests, mentally matching up the Main Scenario quests with your Class quests for your RP. And then once you get to the point where both characters are the same point, you just switch back to Character A and continue on. Past that point, there's only one CS where your starter Archons interact with you, and the event is almost identical in context between the three options... and maybe one line of text in another is slightly altered (NPC says something along the lines of "and you've already met X").
Anyways, that's my thoughts on the matter. Personally, if you really have no plans for the first fifteen levels and related Main Scenario, I'd just go with picking your starting city, leveling the affiliated class, and then go for your preferred class and start RPing from that point. The other way, it can be done but if you're not mentally prepared for it you could run the risk of burning yourself out.
Moving on to the actual topic, though... Unless you're planning to let the first fifteen or so levels and the Main Scenario have a Big Influence on your character, there's no real reason (that I can think of) that you can't just pick the city you want. CNJ, THM, and ACN are all complimentary classes, you're likely to want to get all three up to at least 15 for cross-classing skills and Job requirements. You can also make a bit of nice money this way, by holding onto the gear you get during your first 1-15 leveling spree, and taking the Allagean coin rewards when you run the other two  classes.
As for which Archon you're dealing with... as far as I've seen, once you get past your Envoy mission it's all sort of moot. You deal with whatever Archon is already paired for the region you're currently questing in (Y'shtola for Limsa regions, Yda and Pap...something-or-other for Gridanian regions, Thancred for Thanalan). There might be slight text variations in cutscenes, but you'd really have to look for them.
Now... if you're wanting those first fifteen levels/Main Scenario stuff to have effect on your character... Gridania/CNJ and Uld'dah/THM are easy. With a bit of luck or with an escort, you can run between Gridania and Ul'dah at level 1. Pick the city you want to do the Main Scenario with, run and get the job you want to use, come back to the city you chose, and then just work it into your story that you periodically need to travel to do your class quests.
Limsa classes and Main Scenario stuff with another city as your starter... the way I see it, it would require some more working that you may or may not be willing to do. Essentially... you'd have to run two characters until past the Envoy quests. Character A being the one you're going to keep, grind that up to where you get your airship pass, move to Limsa, then grind up to fifteen again on ACN. Then make Character B with a similar name and appearance, have them start out as ACN, and then level up through the Envoy quests, mentally matching up the Main Scenario quests with your Class quests for your RP. And then once you get to the point where both characters are the same point, you just switch back to Character A and continue on. Past that point, there's only one CS where your starter Archons interact with you, and the event is almost identical in context between the three options... and maybe one line of text in another is slightly altered (NPC says something along the lines of "and you've already met X").
Anyways, that's my thoughts on the matter. Personally, if you really have no plans for the first fifteen levels and related Main Scenario, I'd just go with picking your starting city, leveling the affiliated class, and then go for your preferred class and start RPing from that point. The other way, it can be done but if you're not mentally prepared for it you could run the risk of burning yourself out.