The first question you've asked is covered by the TSE canonical in which it explains that:
The rule of thumb is six statements over a period of six months and the six month period should end with the most recent statement prior to submitting the application. Some people can establish most of the above with three to six months of account history, but first-time applicants and those with borderline cases should submit more.
It goes on to point to the UK Apply for a Standard Visitor visa: step by step:
The first item is "bank statements" and this ties in with the text on the main page , which says:
evidence that you can support yourself during your trip, for example bank statements or payslips for the last 6 months.
While time between payment of the fee and scheduling an appointment is not specified, booking the earliest available or convenient slot is anticipated. As you can apply only up to 90 days in advance of your date of travel, postponing or delaying may be unwise.