Which type of screen mesh do you recommend for my porch screen system?

Screen recommendations can differ based on what you're looking for and the system you decide to install. Here are a few suggestions for you -

ScreenEze/SnapTrack - BetterVue, Charcoal Fiberglass, 20x20 No-See-Um, Pool and Patio, and Super Screen 

Screen Tight - BetterVue, Charcoal Fiberglass, 20x20 No-See-Um, Pool and Patio, Super Screen, Pet Screen, and Solar Screen

Fast Track/Mini Track/Screen Wall - BetterVue, Charcoal Fiberglass, 20x20 No-See-Um, and Pool and Patio.