The setup your school has is for centrally managing all of those APs. The decision to roam to a different AP is up to the client.
For example, with the Cisco controllers, you can determine what SSIDs go on what AP, what power level they should operate as well as what frequency, and even provide guest wireless access from the same APs on the internal network without granting the guests internal access.
For using standard home equipment, do what Alrescha says. Just plug them together into a switch and put the same configuration on each AP, with the exception of channel. I believe Apple's gear can auto-select the channel, similar to what Cisco does. I know I have roamed between my APs with some TCP traffic going (mainly VPN to work) and never had an issue.
Every time you repeat/extend a wireless signal, the bandwidth gets cut in half. So if you repeat/extend using two additional APs, you will now have 1/4 of the bandwidth you started with. Having 7 extenders will cut your bandwidth to 1/128th of the original speed. So, if you have a 100Mb link, you just cut it down to approximately 780Kb.