Agree, in summary: it is necessary to lower the ratio so that the slaves have better performance.
Taking that into account, what type of relationship is the best? I guess it would be broken or am I wrong?
very much depends on the location where you want to place the girl in question. each has kind of a 'demand' listed below the icon.. i think it's called Hobby or such..? that's the preferred in that location. could be Peach skin, D-cup+, Brown hair and Hateful, or something else. the more of those match (then highlighted) the more income in that location. thus, you may want to 'steer' a girl into Broken, or mabye into Obedient for a different place, and buy the 'Change Hair colour' option. changing the skin isn't possible.
before buying the Auto-Turf (honestly i never use it), it's always a good idea to recheck the girls after a few ingame weeks, latest when they've reached 100% Loyality, for maybe a better matched location with higher income. also to keep in mind, traits like 'Slutty Type' etc. require the girl to have performed a certain action a certain amount of times
(in this example '100x vag sex') to trigger the status effect, so better recheck once more. it's money on the line, think business.
the prize is the company chick they've given you for erm, assistance. hit #1 in the rankings and get your 'assistance' alright.
it might well be that you end up with all Hateful virgins which only give handjobs and still reach all top scores and medals in the Annual. it's a long way to that, and takes quite some skills/stats juggling.