If you pay more than the minimum relay fee (currently 0.00005), and a little bit more than the estimated fee for confirmation in 25 blocks (estimatefee 25) then your transaction will get included in a block within an hour or two, almost guaranteed. Free transactions (the ones without a tx fee) still get included provided the priority is very high.

Transactions are broadcast in seconds, and after about 10 seconds, if there is no double-spend attempts and if the minimum fees are included, you can be sure that particular transaction will get confirmed. That's how bitpay and other bitcoin payment processors work. They don't need to wait for a block or a confirmation.

Only small websites like bitcoin casinos wait for a block or more before allowing you to play. Some exchanges wait for 3 confirmations or more.