whats the best way to reglue record covers

Albert, I prefer to use a white PVA adhesive like Elmer's and there's a trick to keeping errant glue from wreaking havoc. Cut a thin sheet of cardboard sized to just barely fit inside the jacket and wrap it with wax paper. Or, you can use silicone release paper like you use to protect a dry mount press platen when you dry mount photographs, it's thicker than wax paper. The non stick surface will protect the inner surfaces from sticking together as the glue dries.

I've always found "Duco Cement" to work well. It's a multipurpose household glue, but it seems to work extremely well for both record covers and split book bindings. Readily available at most hardware stores.

I use my kid's school glue sticks. They work very well.

I have used glue sticks with good results as well. No mess, put tht glue right where you want it.

When I ran my used LP store I invested in a double sided adhesive tape gun, not sure if they are still available. It would be the same thickness tape as the inside lip of most LPs(especially European covers)except the hard cardboarded original 60-70's LPs from the US. I found this to be the best method no mess with glues etc and least impact on the covers themselves.
Roman