If self-muling does it make sense to start with a Barbarian?
Solution 1:
If you want to play a Paladin, I don't see why it makes sense to spend the huge amount of time to try to create a Barbarian with max magic find to get equipment for him. Until you are near max level with your paladin, you would almost certainly increase in power faster by playing your paladin and using whatever gear drops for him, than by playing the barbarian and passing the equipment over to your paladin.
Think of it this way. Let's say that you want to get some great level 70 gear for your Paladin (gear is a lot less important at lower levels, so it is unlikely that you need to worry about that). I don't recall how long it takes to level up characters, but let us say that it normally takes 40 hours to level a character to 70. So you spend 40 hours leveling your barbarian, and now you spend 10 hours doing MF runs with him to get stuff for your paladin.
Now you need to START leveling your paladin. You got some cool gear to pass him, so now it only takes you 25 hours to level him up. So at the end of 75 hours, you have a level 70 paladin with some nice gear.
But if you had spent all 75 hours on your paladin, he would probably be level 90, and probably have much better gear as well (simply by having spent more time fighting high level enemies).
That sort of strategy only seems to make sense if you want to gear up a lot of characters and so you can recoup all the time spent getting your barbarian up to a high enough level over multiple other characters.
Solution 2:
Even though a Barbarian can potentially obtain the highest magic find possible of all characters, this is a VERY, VERY expensive build, one that shouldn't be done until you get some decent items that you can trade for your barbarian's gear. I believe if you're going for a MF barbarian, that requires using the "Find Item" skill where you're expected to carry dual Crystal Swords with 6 Ist runes in each along with other expensive components. Since you really can't kill anything with two Crystal Swords, you also have to gear up your mercenary to the point where it can kill monsters in hell easily (usually good enough to kill Hell cows if you're hunting for items).
Of course, that is slightly overkill - you'd be good with a Barbarian (or any other magic find character build) with around 300-400% MF, as increasing your magic find results in diminishing returns. However, since a MF Barbarian is considered a luxury build, you usually want to max out your MF.
Personally, every time I start over in Diablo II I make a Sorceress as my first character to magic find, and then go with a more expensive character (such as a Paladin) once I have better gear, but it all depends on what sort of Paladin you're planning on making, and how you're planning on playing the game (solo, multiplayer, what you're doing with your character, etc.). While pumping about 75 hours into your Paladin to get to level 90 is nice, that is no guarantee that you will have good enough items to solo Hell by yourself.
And as for your last point, it is equally dangerous to self mule with any character. Transfer at your own risk :).