If your struggling to get started, I've put together an optimal start guide, to get you going on your JA3 journey will all the tools you'll need to succeed.

On a side note, I'd love to hear what you'd change to make things more optimal.

Included in the guide are:
IMP setup - Your primary leader/marksman for the early game.
Early 14 day hires - You save money by going long on contracts, which is obviously optimal, but that restricts choices to only a few mercs early.

There are definitely some optimal choices if you want to meet all the checks from the start, but I think pretty much any selection of mercs is viable as it's an easy(ish) game.

In terms of optimal at the start:

Optimal for Explosives / Wisdom: Barry - It's not even close.
Optimal for Mechanical / Wisdom: Livewire - Once again, stats for cost, she's untouchable.
Optimal for Medical / Wisdom: MD - Once again, this isn't much of a contest either.

These three are not only cheap, their primary skill with high wisdom means they will always be at the front when it comes to their respective niche and you don't risk failing any of the games checks. These are the characters that ensure you don't miss or fail anything and all of them can be trained over time to be monsters, thanks to that high wisdom.

Now - the other question is "What is optimal for making the enemy dead" which is a very different question. Now your thinking about characters like:

Fox, Buns, Barry (Only person on both lists, which is why everyone recommends him), vicky (2Handed), Shadow + SMG, Ivan + 3AP cheese, and so on and so forth.

How "needed" optimal for combat characters are is going to depend on your skill level. The more skilled you are, the more easily you'll be able to go without getting of these "optimal for combat" mercs.

You can find the video guide here:

https://youtu.be/QueRwBYTn3g