I was playing MM VII when I bumped into a magic store, (in Deyja, I think), that had a black potion of accuracy for sale! This seemed incredible! I suppose the 5000 gold price tag was justified, though that was all the money I had.

The tricky part is, who do I give it to? I could give it to my warrior types, but that might make other characters useless in melee by comparison. I could give it to my cleric, who can't hit the broadside of a barn, but I don't know that I want to use it to fill out a weakness. In the end I never decided who to give it to, and it just sits in my inventory, being stared at occasionally.

And what a wacky imbalance of stats it makes. Suddenly you have 3 characters with an average accuracy of 15, and one character with 60+ accuracy. It's kind of comical, really.

I gotta say, it's pretty interesting having this kind of thing so freely available in an RPG. In a D&D game you would hardly EVER see an item give you even a tiny permanent increase in a stat. Even items that give you a temporary bonus cost boatloads. In M&M, you'll casually bump into +2 barrels in ordinary dungeons. Of course, a single point doesn't go as far by comparison, but it's still interesting how casual it is.

I also assume black potions will be available at future points too, in which case, I will not be able to afford them regularly. Unless I start running into an overwhelming amount of income, somehow.

You can find many black potions in shops. Be sure to check them regularly - when the region respawns new items can be found in shops.

As for accuracy potion: give it to a person who is missing most of his attacks and can do considerable amount of damage with melee weapon. For example sorcerer's aim is probably really bad but what's the point in increasing it? He won't hurt your enemies much with his staff/dagger.

A short answer: Give it to whichever of your characters is hardest hitting.
Longer: Like Ghorpm said, anyone who's missing benefits from accuracy, but there's not much point giving it to a sorcerer because even if he did hit more, it wouldn't be worth much.

Black potions can actually be pretty easy to come by, especially if you have a Druid who can learn Grand Master Alchemy and mix your own.
Otherwise, it's worth checking the shops very regularly (especially in The Pit and Celeste) and if I remember correctly, there are people in houses who will offer to mix one for you if you give them the correct reagents (this is definitely true of MM8, not 100% positive if it's in MM7 too)

Magic shops in deya and bracada, can sell items of the best quality, including rare spells and black potions.

Clanker's Lab has some; and precious ores can be transformed to black potions sometimes. But I usually used them to get deficit characters to pass various challenges. I can't remember using them in a fight.

Bob

You know, I was just remembering, I'm pretty sure Deyja ripped me off. I kind of remember that the asking prices was WAY more than the base price. I suppose now it might be worth raising my Deyja faction, though I don't know how just yet. The only dungeon there I can think of is that fortress full of mad amounts of undead, which I run away from. I remember that Stone City was a ripoff until I did one quest. Now they gives me the best prices of anywhere!

Did you choose the path of light? If so you will never be a popular person in Deyja nor in the Pit. Of course it works other way around with Bracada and Celeste.

Just have someone train their merchant skill. The shops I mentioned have the most steep prices, because you can get to them right at the start, and with like 20k gold saved you can buy yourself ring with powerful enchantment or wand of shrapmetal, black potions or something. This makes early game too easy if you exploit it.