There is at least one agency on the net with collectibles insurance experience. It makes little sense to have an appraiser tediously and expensively evaluate each item in the collection unless you expect a disaster that day. Record prices shift constantly, and your aim is to cover the collection. Use your experience to come up with an overall number. Price guides can be helpful.
Some libraries have files of old dealer lists.
Round the numbers up a bit to allow for appreciation and add them up. Count the number of discs as well and add that to your data. Use an appraiser to help get a feel for the oddball stuff and items which might be of considerable worth such as Beatles and Elvis records, where edition and condition make the value spread so wide that expert advice is often necessary. Add this to your other numbers, and insure for that amount. Add to your coverage if your collection is growing significantly.