I've toyed around with an Alchemist class...an alchemist theme [like 5e's "backgrounds" but with more usable/growing utility in my homebrew system]...an Alchemist as a Rogue subclass...I love the idea/concept for a character in a D&D-type fantasy RPG (particularly if or whether you're running in a lower magic setting or not).
Using charcoal was an effective poison remedy for a very long time...not 100% IRL, of course, but this is D&D. I would absolutely put Antitoxin on the list. Potion of healing, I'd leave to the herbalists. Generating poison makes sense as well...plenty of metals, stones, acids, and combinations thereof than can be deadly if ingested.
I think the simplest way would be for a "concoction" progression mechanic. Begin with 1 or 2 + Int. modifier or Prof bonus or however many you think reasonable mixtures that the Alchemist can make that duplicate the effects of [a list of "cherry picked" to make sense or any] a Cantrip level spell. A few levels later, let them begin to accumulate 1st level spell effects.
Regardless of the spell description these magic effects, however, all require a successful "attack" (thrown, poured, whatever, you have to hit/apply the target with the material/mixture/liquid) roll and effect a 10' diameter (5' radius from impact) space.
I would be holding off on homunculus creation til a mid-level feature. Other features should be generally in line with transmuter specialist mage abilities.
Off the top of my head, I'd make up something like this...
Alchemist
Level: Distillates You add one concoction of a level you can use each level thereafter
@1st: Choose 3: Acid Splash, Light, Mending, Produce Flame, Poison Spray, Shillelagh (a mixture/oil that can be applied to a wood weapon to harden/give it the damage boost)
@3rd: Choose 2: Antitoxin, Detect Magic, Detect Poison & Disease, Fog Cloud, Grease, Sleep (gas bomb)
@5th: Choose 2: Arcane Lock, Darkness, Hold Person, Magic Weapon, Shatter, Web
@7th: Choose 1: Dispel Magic, Fireball, Protection from Energy, Stinking Cloud
@9th: Choose 1: Conjure Minor Elementals, Fabricate, Stoneskin, Wall of Fire