But the bad...
The economic system is just bad for the way the game works. Earning money is hard as hell and so RNG dependent, that I can't really wrap my head around it. There seems to be no consistency in costumers - one night you may get 10 guys wanting whatever (C's all around), the next 3 nights you may get 2-3 guys all wanting A's and in the exact thing you don't have. Since barring the weekend there is no way to actually anticipate how many clients you'll have, my profits went all over the board. +2000 to -800. Yes, I'm earning money, but considering I have ~50 days to repair the place for the first quest (~16 000 in total in investments), the global map game starts in the midst of that same thing (5000+ for mercs), and I can barely scrape around 800 per night on average. Yeah, I managed the first quest. Failed the second one (gain 15 000). The economic side of things felt almost meant to be one of those games you just try and try again.
PS: I love the red-haired girl, but the time it takes for her to become useful is just horrendous. She's a dancer and that's it. I just don't have the money to train her to be good and pay her her salary.
PPS: Does the talent for 30% chance to serve a costumer even if not covering the requirements for them even work? Doesn't seem so for me.
The economy is pretty easy.
My initial spend goes on repairs, 5x of food and drink, 2x training room, the training books, one of the training aids and an upgrade to the master bedroom. Since this gives you the energy to interact with all three of the girls everyday. You should definately buy the idol to reduce losses from theft.
If a girl is working spend time cheering her up, happy girls are profitable girls or if they are rotated out for training improve their sex skills. I always rest all of the girls for a day just before the weekend so they go into the the most profitable part of the week with full health, endurance and mood.
During the night service phase I try to keep Fudeyo in reserve for the client looking for higher ranks. This also allows her to be relatively fresh for the first day of the weekday. Early game I rotate her and Saka as my courtesans during the week, with Yura ready to step in if one of them is too tired to work. You can not service all the clients all the time. I also avoid the rough sex maniacs as they wreck the girls physically and mentally in the early game and they don't have the skills and talents to get a decent profit.
Improvements I go for early on are things that help training such as the mirror, perfume etc. things that save money, better brooms, armor. Also relatively cheap things like bath salts, towels. The first big repair is the bath it will bring in 2-300 a day, follow it up with the bath salts mentioned earlier. One thing that I have found isn't worth early investment in is guest rooms. Their profits are highly dependent on reputation which is poor early in the game. Investing in common yujo is another steady earner.
By mid game the Red Petal should break even or turn a small profit even with no girls working.
You are right Mei is best working as a dancer but she certainly pays her way at "Dance C" she will bring in 800-1200 per night at the weekend and 4-800 during the week. I pair her with Fudeyo. Train her in anal for the biggest fetish boost and then work on her Exposure skill once you unlock extra-naughty she will pull in over 2000 per performance on a good night.
The 30% general skill talent does work and I have seen it trigger.