What stats, if any, are we looking for in an elf we want to employ for ourselves?
There are no stat requirements except for basic level of obey (50+) which is easy to get and they're in the top three requests that never go on cooldown.
The first request is the main story directive and not related the employment.
The second request is to employ the elf in your training team which just adds to the employee count (X employees needed for some upgrades), a small boost to all government sectors, and a small boost to income.
The third request is to release the elf to their home area. This grants some time MP for your assistant and later an upgrade will raise the development of that area based on the released elf's knowledge and training.
The next six requests are for the various government sectors and employing the elves there can give you gun skills.
The last three requests are randomly generated for a government sector, but pay more.