Here are some notes I took on what has worked for me. I don't guarantee they're optimal but they're good enough you can be successful in the game.
First, make sure you have at least 1-2 girls who will work for $300 per day or less. Edit the YML files if necessary and lower their popularity.
Buy stage 1 and rooms 1 and hire one girl.
Buy bar 1 and supplies to get through the first night. If you have 3 girls, you probably can sell 150 drinks.
If you have money left, buy rooms 2 and hire no more than 2 more. Keep salary overhead as close to $600 as you can early on.
Buy the book on persuasion and read it. Repeat every day. Advance time and read the book more to increase your persuasion skills. This makes it more likely training will be successful.
At around 17:00, visit the girls and train them. To increase their openness, appeal to their highest stat. You can't train after 19:30.
Lewdness: appeal to excitement/fun
Boasting: appeal to money
Obedience: appeal to satisfying customers
Don't spend all your money and leave some buffer until you're comfortable with how much profit you're able to make.
At 20:00, open the club.
You can use the arrow to simulate the night without having to watch the whole thing.
You should find you turned a small profit, around $400-$450.
Buy Bar 2 before stage 2. The money is in the bar early on. There's no point in having stage 2 until you have at least one girl who will pose (openness 6).
Bar 2 really increases the profit. You probably can't afford to max the cigars, but buy as many cigars as you can while leaving $600 left to pay salary.
Now you should turn a better profit. Stock up on supplies as much as you can while leaving $600 left for salaries.
At this point it may make sense to hire another girl so you have three available.
Repeat, leaving enough to cover salaries.
When a girl gets to an openness of 10, give her a gift. She becomes self training. You can still train to speed her along, but it's not required at that point.
When you're turning enough profit to be able to buy maximum supplies, hire enough girls to have 6. But stay as low budget as possible this early.
Around day 9, you should have enough for stage 2, and most of your dancers willing to take advantage of it. Don't buy stage 2 until you can buy supplies and the stage and have enough left to cover salaries (at least $1200).
At this point, it probably makes the most sense to buy bath 1, gym 1, VIP 1, bar 3, and rooms 3 in that order and start hiring more girls. The profits are rolling in at this point that it's hard to make mistakes.
And at this point, you're making enough you can buy improvements to make the game more fun. Bar 3 is the fastest path to money, but you probably want stage 2 and bath 1 first. You'll need VIP 1 as well before you can buy rooms 3 and hire more girls.