Tower = Real ATC, therefore your life will be more ordered. Therefore, your flow will be like this:
Who you are, where you are, what you want.
So your requests will be:
Airfield Information - Start for circuits - Taxi.
When ready for departure, say so.
Then it will be requests again:
Downwind for touch and go or full stop.
If you trim the plane you will be able to relax on the flying bit for a few seconds and do the radio. If they speak too fast, they'll slow up as soon as you ask. Throughout the detail, you may be passed traffic information, be requested to orbit or report certain positions. The latter are very simple calls like: "G-AC finals".
But as with most things to do with flying, take it easy.
PM
PS. As a PPL holder I always found radio difficult until I used "who, where, what."