Once you've defeated Ultros, you'll find yourself in control of Mog on a black screen with a save point and your various party members arrayed below. Unfortunately, you cannot steal Mog's gear at this point. It is a good move to save before you do anything else. Talking to a set of party members will begin one of three scenarios that need to be completed to progress in the game. All three must be completed, but you can do them in any order. There are a number of considerations as to which order you should complete scenarios in (though for simplicity, this guide simply moves from left to right).
Gear Considerations
Though you can't unequip party members from other scenarios, all three share the same item list, so items won in one scenario can be used in the next one. It is possible to unequip characters before the end of a scenario, but this doesn't work so well in Locke's scenario since it ends with a boss fight. This is especially pertinent since most of the treasure found in that scenario will likely be used to equip Celes. You won't find a lot of treasure to transfer in Terra's scenario at all.
The outlier, then, is Sabin's scenario. While most of the treasure you find is for the party members in that scenario, it ends with a trip to Nikeah where you can pick up significant upgrades for your other party members. As a result, completing Sabin's scenario early can give you a leg up during the others.
Veldt Considerations
On the other hand, Sabin will meet Gau during his scenario. Gau learns abilities by fighting creatures that you've met before elsewhere on the Veldt. Any creatures fought in scenarios done before Sabin's will appear here, giving Gau a lot more options for Rages to learn.
So What Should I Do?
I recommend doing Sabin's scenario last. It is the longest of the three, and having more creatures on the Veldt is helpful in the long term, since it will be some time before you can take Gau back there. Plus, neither of the other scenarios has such difficult encounters that they need upgrades from Nikeah. The next section of the game may, but if you do Sabin's scenario last, you'll have all the money accumulated from all three scenarios to spend there.
As for the first two, it doesn't matter very much. Locke will find some nice relics that may be of use, so it makes sense to do his scenario first. Plus, that's how I wrote the guide, so it's easier to navigate that way!
Whatever you choose, use one of the links below to proceed to the guide for that scenario: