Hi,
Welcome to the forum. A good decision buying a boat, hopefully you'll have loads of fun.
I can personally recommend Nick at BoatBility based at Port solent for courses, he can either supply boat and equipment or he will do it for a reduced cost on yours which obviously gives you slightly better experience for when alone. I did a advanced powerboat course with him and it was great!
I am local, work pretty much at Port Solent, ( just the other side of the big field) and the boat is kept just down the road. The channel in and out of port Solent can be tricky for the first few times in and out as it shallows very quickly!! Be warned!!
The guys at the lock are very helpful and will assist where necessary.
As for exploring the Solent, as Colin says, get some charts and read them for where you want to go, there are some parts that will catch you out!! Mind the sandbank at ryde... Some of us have got to know it quite well!
Plenty of info on here, just ask..!