[...] What work/research should I do up front in order to feel confident I will be getting a fair price?
You can ask money.SE or history.SE by giving details of the coins, if you feel that doesn't bring privacy or security issues.
You can and should refer directly some renowned book; in the past I've personally found the Krause Catalogues useful after finding a couple coins at grandpa's and wanting to sell. I would definitely recommend you pick an old copy of that or an alternative book. Should prove cheap and cost effective.
Sometimes at town's coins dealer they can assist you with finding the proper book. Krause books are a fairly decent international knowledge, but there might be local books more relevant to your case.
What you don't want to do, you got it right, is to go the coins dealer before doing your private research. Anyway hopefully it won't make a difference about the price you get.
It's a specialized market of big hands, and large bid-ask spread; the smallest the intrinsic precious metal value of the coins, the larger the spread and amateur trader's risk.