As for payment, most every inspector will require payment immediately upon completion of the inspection. Inspections are generally not included in the purchase, or in the closing costs of the purchase. Most inspectors will take cash, credit card or check, and prices vary, usually in the range of $300 to $450, depending on a number of factors, especially the size of the house. Inspections will usually take several hours, and it is good to be present while it is underway, usually for the final half-hour or so, to be shown any deficiencies or anomalies that the inspector has found.
Depending on the age of the structure, additional specific inspections might be advisable, especially if there are significant electrical, plumbing, HVAC, or foundation issues discovered. Most inspectors are not fully qualified to make such detailed assessments. If the house you are interested in is rather old, you would probably want to budget for some of these also.
Home inspections aren't required, they don't always find every defect, and the cost is not recoverable if defects are found that cause the purchase contract to be cancelled. That said, they are very good insurance against unpleasant and expensive surprises that can be found through inspection. (Even on the purchase of a new home, defects in construction can be found!) If defects are found prior to purchase, the repairs can usually be negotiated for a more favorable transaction for both parties.
Do you have an agent representing you? If not I'd love to help.