To all the people who want to cherry-pick effects, being able to pick effects would be unbalancing. There are both good and bad effects in order to make you think harder about your potions/poisons. You can't have a perfect potion every time. You should be able to specify whether you want a potion or a poison though.
I think it could be balanced. What if it worked like this:
1) You research potion recipes using an interface very similar to the spellmaker (you can also buy recipes from NPCs), and costing gold just like spellmaking.
2) You only pick the desired effects for your potion. The magnitudes, durations, etc. are considered to formulate "potion power".
3) The game randomly generates a list of ingredients based on the spell effects you specified -- each spell effect has a table of ingredients that it can add to the recipe. The more powerful the effects, the more powerful and expensive the ingredients you need, and you may need several for one potion.
4) The game also creates a hidden formula for undesired side effects for that potion, up to the same power, based on the ingredients it picked.
5) When you actually go to create a potion, there is an "ideal power" which is calculated from your Alchemy skill and stats (and possibly your equipment as well). If the potion power is less than or equal to your ideal power, you create a potion with only the desired effects. If the potion power is over twice your ideal power, you can't create the potion at all. Otherwise, your potion has undesired effects. The power of the undesired effects is equal to the difference between the power of the potion and your ideal power. That is, if a potion has a power of 800, and your ideal power is 500, you will have 300 points worth of side effects, as determined by the formula created in the previous step.
6) Rather than reducing undesired effects, poisons would function with reduced effectiveness between the ideal value and twice the ideal value.