The first fan you showed looks fairly cheap. If noise isn't a concern for you, than the prime stat you need to be looking at is CFM - how much air the fan pushes in a minute. That particular fan pushes only 21CFM, I've seen 80MM fans push more air than that and aren't that much more expensive. If noise cancellation is a concern, then look at the dB(decibels, a way of measuring noise) that the fan produces, the lesser the better. There are also variable speed fans out there where you can control the speed - or if it uses a 3 pin power connector on the motherboard, your motherboard may control their speed that way using temperature sensors in various locations on the motherboard.
As for the second item, either way your computer is going to cool down after it turns off, regardless if the fans are on or not it's just a matter of how fast it does so in this scenario. However, if remnant heat from when the machine was on turns out to be a problem, then it'd be a worthwhile investment(after all,it's only 10$).
As for the second item, either way your computer is going to cool down after it turns off, regardless if the fans are on or not it's just a matter of how fast it does so in this scenario. However, if remnant heat from when the machine was on turns out to be a problem, then it'd be a worthwhile investment(after all,it's only 10$).