Congratulations.
This is a very common problem for a non-collector. There are many similar posts on this site and the best advice is to get hold of a local stamp club. I am a member of the Rochester Philatelic Association in upstate NY and we typically meet twice a month except during the summer. We have a casual discussion for ~1 hour before each meeting and about 3 times a year, someone like you brings in a collection for general evaluation and advice. In many cases the stamps are common but sometimes there are some real treasures. Often there are club members with good expertise in the ares of the collection and sound advice is offered.
If you don't live near a local club, try getting hold of local dealer and have him/her evaluate the collection for an insurance appraisal. Tell them you have no interest in selling the collection (to prevent a low estimate). This will cost you somewhat for the dealer's time but it will pay for itself with interest when you decide to sell the collection.
The last choice, and the worst, is to get a set of catalogs and try to evaluate the collection yourself. There is a lot more to evaluating stamps than looking up prices in a current catalog. Condition is very important and can affect the values by a factor of 10 (up or down).
Then there's some consideration about how you are going to sell it. If it's sold in bulk lots, the cost of labor to break down the collection must be factored in. Multiple copies of the same stamp will also cause the price to drop since it takes a lot of time to get rid of duplicates. For good quality material, dealers will generally offer 10-35% of catalog but collectors will pay 50-75%. Of course, you have to find those collectors. Again, the stamp club or
ebay (and other sites) offers some opportunity. However, exceptional quality and/or very rare items should be sold by auction firms to get the best return.
Good luck!