Other will tell you about Cris and HPI etc, but insurance:-
You need to tell your car insurer that you have modified the car by adding a tow bar, and presuming they have not added any other limiting factors, the whilst the caravan is attached to the car it is covered for third party claims as a road vehicle. It is always wise to check your insurance policy.
But there is no legal requirement to have insurance on the caravan or its contents, but it is a wise move, and if you have used a finance package to buy it they usually require you to have insurance as one of their T&C's.
As with all insurances, there are many policies from different suppliers, so you need to do some homework to work out which cover is best for you. Often the true worth of a policy is how much hassle it is to use, should you need to make a claim, and sadly the DEFACTQ rating does not cover that aspect, but you can reasonably assume the cheaper a policy is the harder they will try not to pay out.
Consequently I would suggest you should look at those companies with a good reputation, and for caravans, both of the main clubs have policies which are more specifically tailored to caravanning, and there are some other well respected companies such as the NFU and other established names, It may be a little more expensive, but they are generally more helpful and a lot less hassle.