I'm playing an alchemist at the moment, though still only low level. Playing him as an arrogant intellectual Frankenstein type, complete with vengeful creepy renegade experiment on his trail. Everything is an alchemical or pharmaceutical treatment, he casts Guidance by taking a big snort of a powdered stimulant compound of his own concoction, etc. Enjoys dissecting any fallen foes that he find interesting.
Mechanically, I'm not really coming to grips with it yet. You have a broad arsenal of abilities, but it seems to be a mile wide and an inch deep, and they're largely out of combat or utility abilities. In a combat-heavy campaign, you often feel like you have no big gun to pull out in a serious fight. Other artificer subclasses get a major combat feature early on, but alchemists don't really. You're only a half caster so your attack spells are never going to be spectacular, especially since i rolled fairly mediocre stats and my Int bonus is nothing to write home about. I still find my crossbow (for 1d8+2 damage...) is a go-to attack option most of the time. Your spell list has ok combat options like Faerie Fire etc, but you just have so few spell slots that you have to be stingy with them because sooner or later the party will really need that Healing Word or Feather Fall.
Experimental Elixir is a bit of a mixed bag. At low level, it can be really good. No-concentration 10 minute duration flight at level 3 for the cost of a 1st level spell slot is very useful, even if it's low speed. But it's yet more competition for your very limited supply of spells slots, and like many of your abilities, it's a utility, out-of-combat thing, so it doesn't solve the 'um, I shoot it with my crossbow i guess?' problem. At a higher level, most of the elixir options are going to become pretty obsolete I think, although +1d4 on all saves and attacks never gets old. WotC often has this problem with subclasses with random features - the random table is too small, so the randomness loses its novelty and unpredictability fast. Wild Magic barbarian was the same. Spirit bard was a bit better, because it used a bigger dice and unlocked more powerful options as you gained in level. Still, you could probably homebrew an expanded elixir table to make things more interesting.
As for infusions, i basically took enhanced defence and replicate bag of holding, and have never used any others. I also know Create Homonculus and Enhanced Weapon, but my two standards are just too good to ever swap out. I can think of times a homonculus might be useful, but we already have a familiar in the party which can do the same things better, in general.
I think the key will be to embrace being a support character who does most of their work out of combat, or in preparation for combat. As a half-caster you're never going to have big attack spells to throw around, and unlike armorers or battlesmiths you'll never get extra attack so combat won't be your go either. But you've got a moderate bit of healing to throw around, and Invisibility and Rope Trick never go out of style, while Heat Metal and Acid Splash give you at least something to do in combat once Alchemical Savant kicks in.
As for the future build, I'm not too sure. I just hit 4th level and am wondering what to do with my feat/ASI. Increasing Int is the obvious thing to do, but even though some class abilities are int-based, is it really worth it for a half-caster? Metamagic Adept with Twin Spell could be useful for a support character to double up on the buffs. Poisoner is very in-character, but poison is expensive to craft and of dubious utility in a Tomb of Annihilation campaign where loads of the enemies are undead, or else dinosaurs with massive Con saves. I could take Skilled and become a sort of quasi-rogue I suppose - we don't have one in the party and artificers already get thieves tools proficiency. Or else I could go with Telekinetic, which would give me a few extra utility and combat options while being half way to an Int increase that i can complete with Telepathic at 8th level.
