Best Glue for LP cover seams?

Make sure the two surfaces you're gluing are clean & have as little oil from hands as possible. A couple firm strokes with with a paper towel should do it or try a swipe with fine grit sandpaper for tough to clean areas. Press it with between something like two heavy hardback books. Don't put so much glue on you glue your album cover to a book.

use a good quality glue stick

UHU Office Glue Pen manufactured in Germany. Ideal for paper & cardboard. This pen can be purchased in the archival/scrapbook supplies ($6.00) @ JoAnne's along with Scotch acid-free clear tape($5.00).

I use Elmer's Glue. A thin bead of glue and a heavy old book placed on the seam for an hour holds the bond.

I second the glue stick. I have to buy a pack every year for my children as part of their school supplies. I've been using one for years and it works well 95% of the time (a few times needed a second application).