Some good advice already posted here by several if not all responding. The only thing I can add which hasn't been stated is that if you are a new and/or low time MEL pilot - committing to a simulator based training initial (such as Simcom) will open up the most amount of underwriting options. If you try and cut corners and use some unknown outfit and train in-aircraft you will have fewer underwriting options for the policy.

Most insurance brokers know that the more options you have quoting a risk the more potential leverage you have in the marketplace with the initial policy - either respects liability limits or premium consideration. Good luck to you.....

Ahhhh...the dreaded double engine failure. I had that last year at SimCom, as well as 1 failing at 200' IMC on take off.

In my experience, insurance $ are going to be a small part of your operating costs. Also, you can't "shop the market" with multiple brokers. That tees off insurance companies. Pick a broker and let them do the work. A couple good ones here on BT.