What Bluetooth profiles are you planning to use?
If you need only low data rate data transmission, then BLE is direction where you probably should look.
Lately I am fan of Cypress PSoC, so I can suggest to try it:
http://www.cypress.com/products/psoc-4-ble-bluetooth-smartOf course Blue gecko also should be ok.
If you need Bluetooth audio (A2DP) or other classic profiles, then it will be more difficult.
Even then I do not suggest to start CSR development, but already pre-programmed modules. (BC127, LAIRD BTM511, WT32i, etc.)
When you say "school project", I understand that that your goal is not to develop best product for mass-production, but to get concept working ASAP.
In that case use of some Bluetooth module can save time and money. (Even in small manufacturing batches (up to 1000pcs), because lot of them comes FCC, IC, CE certified)