The answers here seem not very good. Having played the game a lot, I've found the following:
Recruit everybody. At the start of the game, you will only be able to recruit E-C level soldiers (C's being rare). Better soldiers get posted based on your own rank.
Fire the bad ones. As you progress through the game, you will begin reaching your population limit. While expanding the base is the right thing to do, as you go, you will need to start setting a limits for minimum skill. Don't recruit anyone at that point below a certain level (unless you have to or they have very special development skills needed to progress).
Do not spend MB coins on people. Do not spend MB coins on completing dispatch missions early. You will need these MB coins to expand your FOB's. Per value, that's the best usage because you can drastically increase your population.
As for acquiring the best people, I've found that the best skilled people are spawned in missions. Bases (OKB Zero, Power Plant, Airport) have the next best. Outposts typically don't have very good soldiers. Sending your team to expand via dispatch missions is also good. And complete all missions with an S rank to get a good supply of S soldiers.
Also, I've only got a basic understanding of morale. The easiest way to increase morale is to keep a high amount of money. Do not spend down to 0 GMB. Only buy the weapons you need. You can purchase most low level weapons to find your favorites, but then expand in a controlled capacity (max out 1-3 weapons). Don't go into the field armed to the teeth. Control your support costs by customizing a low level weapon with required upgrades. You spend a ridiculous amount of money taking out high level weapons, and usually a well-modded low level weapon can do everything a high level weapon can.
Specialists, at least with a moderately high level, do not have guaranteed higher stats. Hats indicate classification of soldier, most primarily what weapon they will use, but not necessarily their skill. Mark all enemies and find out their skill. D-Dog is helpful when kidnapping an entire base.
Recruitment is a slow process, and the game seems to limit how fast you can raise at the start.