How can I recruit the most skilled soldiers?
Soldiers with high skills out in the field are rare. Without the scope the best way to determine an estimate of a soldiers skills is to consider their attire. Soldiers that wear high rank hats for example will have better skills than those who wear common hats. However, the scope is your key source of information on soldiers abilities and skills. Upgrade it as soon as possible, check what requirements you are missing, such as a lower than needed level in a particular ability branch of your Mother Base and do what you can to increase the level. Keep in mind that you also get volunteer soldiers after completing missions, so extracting is not the only means to get skilled soldiers.
The population cap per division as well as the overall cap can be raised by building base structors for that division, building a command base structure raises all divisions population cap. Base structures cost resources and GMP, try to go through different interiors and side outposts in free roam to find the materials needed to upgrade your base.
Fulton costs relatively low GMP to use in the field, try to store up on GMP when you know you will need it for Fulton (and resupply drops). You can build up GMP through doing missions, side ops, and operations with your soldiers. Other ways to gain GMP include extracting animals. Try to do missions sneaky and quickly for big GMP points (multiple hundred thousands), so long as you don't spend your points on upgrades that you don't need right away, you will have plenty of points to spare for Fultons. You can also increase your storage capacity and success rate by increasing your Support division in MotherBase.
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.