For alchemy: Gather every alchemy aspect you find, discover all traits (look it up online if you don't want to discover it all on your own), and then make potions and poisons using the ingredients you find the most. Don't use rare ingredients like Columbine for training the skill. Either save them for crafting some of the most powerful potions when you know how, or sell them in a traders guild. The money you'll get from it can buy you more cheap ingredients, which allows you to craft more potions and poisons, thus levelling the skill more.
Also do the daily alchemy writs. You'll get Alchemy xp for crafting the items, as well as for completing the writ. And you may get more ingredients out of it, allowing you to brew some more.
I hope this helped.
You should only need to make one Blue and one Purple for Provisioning, but Gold may have been added since those recipes are now in the game. Oh, and to reach L50 in Provisioning, just make the highest level Green Recipe you can, Blues and Purples do not give more inspiration (other than the very first time you make a Blue or Purple, and probably Gold if the last has an achievement)
As for Alchemy, you need to use every solvent in the game, but some might be hard to find due to the way nodes are scaled. See this to cover every reagent efficiently:
https://forums.elderscrollsonline.com/en/discussion/203575/the-most-efficent-way-alchemy-discovery-and-leveling/p1
This should be correct. I purchased around 10 purple recipes yesterday and I got 1 more level in Provisioning but I am still stuck on Alchemy. I know all the reagent traits and I have all achievements except for the "Collect Homestead items" achievement. And that achievement did not affect the other Tradeskills since I got them in level 10 already. Including Enchantment.Provisioning mastery is blue/purple/gold recipes.
Alchemy is knowledge of reagent traits/achievements.
I could be a little wrong on the achievements part for Alchemy.