I placed an order for the $50 payment to PayPal on January 6, and the order still says "Placed", with no further progress. Since I so infrequently get enough points to order anything, I can't say one way or the other what the time frame was for prior orders.
For Paypal orders they are processed at the beginning of each month, once a month. All orders from the previous month are processed, this can take a variable amount of time due to accounting backup and the fact that all orders are reviewed before they are paid out. Typically you can expect payment by the 10th~ the month after placing. Gift cards however, are generally pretty quick. If you place them between 8am-12pm PST you can expect to have them reviewed and approved within the hour.