I'm prioritizing improvement of the Alchemy and Enchanting skills because they can enhance practically everything else, including each other. I'm focusing on creating potions with a Paralyze effect for use in my travels. The Paralyze effect comes from either: Briar Heart, Canis Root, Gleamblossom (DG), Human Flesh, Imp Stool, Netch Jelly (DB), or Swamp Fungal Pod.
Unfortunately, all of these ingredients, in terms of merchant availability, are either uncommon, rare, or unavailable to be bought. I'd rather not save-scum merchants in the hopes that it pops up in their inventory. I noticed that at least two of the ingredients can be found in the College of Winterhold, but it takes 10 days for their to respawn.
I understand that asking for a route to collect only ingredients for Paralyze would be too narrow, so instead I ask what's a good route to collect alchemy ingredients in general, preferably free.
Update: I rephrase the question from "What's a good route to collect alchemy ingredients?" to "Which buildings have lots of ingredients?" In this way, one may blaze their own route. I presume that all apothecaries have tons of ingredients laying around. If an apothecary doesn't, that's worth noting. What's also worth noting is which apothecary has the best merchant chest.