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.
3 Answers
Finding ingredients in Skyrim is easy. Just go adventure and be perceptive. Ingredients can be found almost everywhere. I usually had to stash all my ingredients in a container next to an alchemy lab whenever I visited a place I owned because they weighted so much.
Below is a description where you will find the paralyze ingredients:
The Swamp fungal pods and Canis root ingredients grow in the Hjaalmarch. You can pick up a lot of ingredients by circling the region every once in a while. Imp stools are found throughout the caves in skyrim. There is a large amount of imp stools in Chillwind Depths, a cave to the south of Dragon Bridge near Hjaalmarch.
Human flesh and briar hearts are rare ingredients. Necromancers use the flesh and briar hearts can sometimes be found in alchemy rooms throughout skyrim. You can also kill Forsworn briar-hearts but they are uncommon and tough.
Gleamblossom can only be found in the Darkfall passage and Forgotten Vale but it's a long trek through an army of falmers.
Finally to acquire netch jelly, you need to fight the netch creatures which can be found along the western and southern coast on Solstheim.
Just to add to Steinin's great answer:
If you have the hearthfire DLC, you can also plant imp stool and swamp fungal pod in a greenhouse or the garden. This makes collecting them MUCH easier. It also respawns quite fast (I think they respawn every 3 days).
Finally, if you don't mind mods that assist in this area, I suggest the Harvest Overhaul mod. It makes more sense to have the chance to collect 2 eyes from a sabertooth and 5-10 flowers from a clump of them than a single ingredient.
Also, keep in mind, to make your alchemy go up the fastest, you'll want to make the most expensive potion so this question may be of some help.
Here are my disorganized notes:
Ingredients stops: College of Winterhold (Hall of Attainment and the Hall of Countenance), Windhelm (White Phial), Solitude (Angeline's Aromatics), Morthal (Thaumaturgist's Hut), Dawnstar (The Mortar and Pestle), Markarth (The Hag's Cure), Riften (Elgrim's Elixirs), Whiterun (Arcadia's Cauldron), Sarethi Farm (The Rift), Blue Palace (Solitude), Mistveil Keep (Riften), Palace of the Kings (Upstairs) (Windhelm)
Try court wizards rooms and places with Alchemy Tables and Arcane Enchanters in general
Unconfirmed: Frostflow Abyss (Winterhold, 516 Chaurus Eggs), Blackreach (Great Lift at Mzinchaleft, Crimson Nirnroot)
Unhelpful, or secretive (difficult to access): Fort Dawnguard (Florentius Baenius (DG)), Volkihar Keep (Feran Sadri (DG)), Dushnikh Yal (Murbul @ Burguk's Longhouse), Mor Khazgur (Sharamph @ Larak's Longhouse), Northwatch Keep (Haafingar), Jorrvaskr Living Quarters (Whiterun), Nightcaller Temple (The Pale, LMW), Talking Stone Camp (Hjaalmarch, LMW),
