Equivalent of US$ 500 for each month applied for.
They no longer use the "$500 USD equivalent in a Turkish bank" rule. You just need to state that you have enough money to live on when you apply online. During your appointment, they may or may not ask you for proof of this, but you should be ready to convince them that you have enough money to live on if they ask. If you are only going to be here for a month or a few months after your visa, they probably won't demand any proof of that kind. And you no longer need to have the money in a Turkish bank.
And once you have applied for a residence permit, you can stay in Turkey using the residence permit application form you can print off after you complete your application online. This will cover you so you can legally stay in Turkey until you receive your residence permit.
You will also need to buy health insurance to cover you during your stay, from a private Turkish insurance company. They only sell the policies for one year at a time, so unfortunately you will have to buy an entire year's coverage. Before you leave, you can go back to the insurance company and get a refund for the unused portion.
There are also some articles about the health insurance requirement on that site.