Waterproof map paper wants a laser jet or a high-quality thermal inkjet that uses pigments instead of dyes. Cheap inkjet printers use water-soluble ink which smears. The alternative is to print on regular paper and then coat it or laminate it (or just not get your map wet). However, if you coat or laminate, it becomes difficult to write on it.
Used to use Nat Geo Aventure Paper but they stopped selling it. Rite in the Rain paper is an inexpensive paper-based waterproof product but is not more resistant to tearing than regular paper. For tactical situations, you can also get tan and light OD green paper. DuraCopy, I-Gage, and Puffin are synthetic papers that are tear resistant. People have even printed on sheets of Tyvec but I can't figure out how to make it feed properly.
All the waterproof papers take writing from a ballpoint pen but it had best be waterproof or it will smear. NONE of them do well with gel pens or markers. Only Rite in the Rain does well with graphite pencil. Have yet to try grease pencil. I like to use 8 mil synthetic over 10 mil for smaller maps because it folds easier. OTOH if you print two-sided, you want 10 mil to prevent bleed through. There is only one thickness of Rite in the Rain.
I prefer to use 8.5x14 (legal size) stock. A double-sided map on legal size printed at 1:24000 usually gives me roughly 10 miles of hiking on one sheet. In terms of ink, less is better so I use economy mode. Using more may cause excess ink to just lay on the surface which can lead to smearing and staining the pocket that contains the map. (Pigment-based inks never fully wash out.) Dye-based ink should ALWAYS be coated or laminated.
https://www.waterproofpaper.com/