Since my eventual first upgrade to the car is likely to be a set of new springs / dampers, will my insurance likely go up, and if so how much has someone paid for it?

Depends on your insurance co

Do you need to tell them, I was only going to speak to mine when i re-mapped it.??

The majority of insurers will want to know of any changes made to the car...

L&V are an exception in this case...