What criteria should I consider for choosing paper for watercolor pencils
One of the first things you’ll want to remember is that you should always be using archival quality acid-free paper. Also, the heavier the paper, the less the paper will wrinkle when wet. In fact, after about 2mm of thickness one will generally be speaking of board, not paper.

Hot pressed papers (and boards) are smoother than cold pressed, and although there are many pulp options, you should really consider 100% cotton rag. Don’t try and be a hero saving the environment - use virgin non-recycled materials.

Many artists attach their watercolor paper to a wooden board with masking tape along all the edges. This prevents the paper from curling too much, however I never liked the fact that the tape generally rips off the top surface of the paper. That’s why I spread acid-free bookbinder’s PVA glue across the back of 350g cold-pressed paper and bond to the smooth side of a sheet of Masonite (HDF) reinforced with a wooden struts, all of which is later used as a backing plate to attach the frame.

My advice specifically for your use case is to use the pencils only when the paper is dry - otherwise you really run the risk of damaging the surface. That and to start using a brush.