So my proposal is not to make alchemy stronger or weaker, more complex or more simple, but just less tedious. The same rough effect for fewer mouse clicks, and less breaks in the flow of combat. So here's some ideas, based on what I guess will be possible and impossible with the CS. The balance may well need significant tweaking for these changes, but it's hard to tell without trying it in practice. I have no intention of adding any new ingredients or new effects or any other sort of "alchemy expanded" sort of thing - I'll leave that to someone else.
The cumbersome UI is the first problem, though it's well outside anything I could do anything about, I think. A semi-translucent quick-access menu for potions, with appropriate filters, would probably be the ideal solution here. I've seen some nice mockups in the UI thread, so I'm sure our talented UI modders will soon give us something more workable here.
Potions
Healing potions - deliver healing over time, perhaps 10 seconds. Total amount of healing for created healing potions increased to compensate, perhaps 50% or even 100%. This will of course significantly weaken the efficacy of using healing potions as an infinite health bar. If you've waited until you're down to a smidgen of health, you're too late. If you're fighting an enemy that's damaging you faster than you're healing, then maybe you should run away. The aim here is to make healing potions less of a "panic button" and reduce the stop-start type of combat it engenders. And to bring it more into line with the healing spell in Restoration.
I have no idea whether this would interact with regeneration potions and fast-healing items; not overly fussed either way, to be honest.
Restore magicka/stamina potions - again, provide a somewhat larger total benefit but over a bit of time (again, perhaps 10 seconds). I feel that a ten-second timeframe for these might actually make them more useful, to sort of match the rate at which they deplete with use. My experience with these potions is limited though, so very open to feedback.
"Resist x"/"fortify x" - I'm inclined to double their duration, if not more. Enough so that you're unlikely to be worried about drinking another one mid-fight. It would be fantastic if someone could mod the UI to actually show your potion effects and how long they have left as well, because it's currently very unwieldy.
Maximum number of active potions at once: Again, may not be possible to separate potion effects from magic effects in general. But it would be nice to limit the currently very easy potion spam.
The alternative approach, which might be easier and better, would be to initiate a quick drinking animation whenever a potion is consumed so that the player can't attack, block or use another potion while the animation proceeds (probably 2-5 seconds) - or at least play the animation when the player is actively in combat, so that there's a risk/reward aspect, and so that you can't chug ten potions at once.
No eating food during combat. Fairly self-explanatory, right? It's conceptually ridiculous, and it promotes the same fiddly stop-start combat that the current healing potions do (as well as tediously ransacking every barrel around for its apples). Food is not terribly useful for healing right now anyway - I think its main use will come with whatever Primary Needs mods people make.
Poisons
Making poisons last. I wonder whether damage health/magicka/stamina poisons ought not to last for more strikes - so that there's no temptation to laboriously re-poison your blade every strike. The "poison lasts for twice as many strikes" perk in the alchemy tree leads me to believe this should be possible. A side-effect of this would be to make daggers (with their swift speed) more useful in combat. My suggestion would be that poison lasts for 5 strikes (or five arrows), ten with the appropriate perk. I would further suggest a restriction on using poisons in combat...the poison will still give an early and powerful edge, and it's one less thing to break the flow of fighting. Not really the sort of thing you can really do in the heat of battle anyway, is it? A less severe alternative would be no poisoning in combat if enemies who have detected you are within a certain range, though this opens up the possibility of a tedious "fight, run away to poison, run back to combat, run away to poison, etc" style of play.
This may also require that selecting a new poison while another is already in effect "overwrites" the previous poison (with a confirmation dialogue), so that new poisons can be selected after short battles from which there's still some poison left.
Make damage health/magicka/stamina potions deliver damage over time by default (again, probably ten seconds). Essentially switch over the "damage health" effect with the "lingering damage health" effect (and for magicka and stamina too). Damage health is the "easier" and more common potion, but I figure a poison that deals all its damage immediately is a rarer and more useful thing. The strengths of the two damage types would have to be rebalanced, but that's okay. Technically, it would be nice to be able to just edit the effects of the two magic effect types without changing anything that references them - but I have no idea whether a seperate magic effect is used for potion effects, and this would be problematic if potions and e.g. traps were referencing the same effect. I would rather avoid editing the individual ingredients if possible. I have no problem with editing the existing "store-bought" potions.
So the overall aim with poisons is that you only poison once per battle before the action starts (so you're never pausing mid-combat), with a stronger overall effect from that given poison; the tradeoff being that you need to have prepared slightly beforehand (sneak helps here, as it should), make multiple hits and survive long enough for that damage to accumulate.
Potion making:
Remove or reduce the relationship between potion value and xp for levelling up. I would like to level up primarily from potions I make for my own use, rather than potions I make for their high value. In particular, increase the xp for making poisons, since they level a character up very slowly. If possible, I'd also be inclined to give xp for failed combinations (at least the first time you try it), to reward experimentation. I'd also reduce the skill requirement for the experimenter perks by 10 each, they're currently so high that only very high-level characters or people who grind alchemy will ever see the higher effects.
May not be possible: a third ingredient with the same effect gives a bonus to the strength/duration of that effect. To promote using a given number of ingredients to create fewer high-quality potions rather than many weak potions.
A basic alchemy sorter. There are satchels at the alchemy stations in each of the homes. A minor edit to give a dialogue that lets you give all/take all ingredients without having to go through each individually.
Anyway that's the basic idea, the actual capabilities of the CS when it arrives may invalidate half of those or open up entirely new options so who knows?