I can't speak to the printing part because I've had a lot of issues finding a printer myself (not for maps, mostly for making my own Filofax printables, but I did also try to print an A4 copy of my world map for my story bible and it did not go well with my old printer. The new Epson XP-520 did a better job of the black & white sketch version (no textures, just hand-drawn stuff) but I haven't tried it on the full-colour texture map yet). I'm also not experienced with commercial maps from either the buyer or seller's end, so I can't help with your decisions in that regard.

For lamination, though, I just bought a Monolith laminator for about £15 on Amazon (this one here). That should be enough to get you started, but you'll probably want to get an industry-ready laminator if you mean to make any serious money with your prints.

I also got a 100 pack of Zoomyo 160 micron laminating pouches for about £10. The resulting laminated pages seem kind of flimsy so you wouldn't be able to write on them without a surface to write on, but it's plenty for my Filofax or if you're printing stuff to hang on a wall, or you're printing something for desk use. 100 pouches will last me a good long while, too, but it's the cost of the pouches you'll really need to worry about in the long term and I don't know if you'll find the return worth it. (It works out around 9.5p per pouch for the pack I got. It costs more if you want thicker sheets, and you'll need a much better laminating machine for that, too. The one is only supposed to deal with 125 micron sheets but did well with these, though, so you might be able to get away with it.)

I haven't used my laminator for full sheets yet because I mostly got it to make my own magnetic bookmarks from sticky notes a la this tutorial in YouTube and reusable shopping list (again for my Filofax). I did have to push the sheets through a few times to get all the bubbles out, but I imagine part of the problem there is all the gaps between the sticky notes. I don't think a full sheet of regular A4 (I think that's what you mean by the 8.5 x 11") printer paper would need nearly as many passes, but thicker photo paper might.

Either way, I would recommend getting a corner chomper if you are going to laminate. Laminated corners can be a serious health hazard to your (or your buyers') hands if you don't soften them up some how.