As the title says, I'm not sure what's considered "enough" stats on an item that would qualify it as suitable for what I need.

The main item I have this problem with is Atma's Impaler. Most champs would get about 40ish damage out of the passive, so in total it'd get you 45 armor, 40 damage, and 15%crit chance. Crit chance I understand, but is 40 damage and 45 armor good enough to warrant buying it versus spending the gold on something like Frozen Mallet instead?

A similar case is Sunfire Cape and Wits End. Is the 40 magic damage make enough difference to warrant the purchase?

It always deppends on the situation and what your enemies are buying or who of them is getting the most kills or doing more damage. If you want to know if it's "enough" you have to put in balance the stats you are given and the amount of gold you are paying for it. If you want to know if Atma's is better than Frozen Mallet well, it deppends on your champion and the specific match you are playing

Atma's is usually combined with a Warmog's Armor but I rarely see that combo anymore. I feel there are better buys.

Sunfire cape is a great item, it screams "attack me" otherwise you'll be dealing 200 aoe magic damage a second in a team fight.

Wit's end is great as well, characters like Shen and Cho'Gath benefit from the attack speed passive + the magic damage on hit, it clears waves very quickly.

Simply put, if you need it, you want it.
If it is efficient on your champion, it is viable and a good purchase depending on the situation.
What are you lacking? What are you planning? What do you need? What does your team require? What are your opponents building? Who are your opponents?? Buy accordingly.
If you buy an item and some stats you don't need, you wasted a good portion of that gold making it not cost efficient. Some items have really strong benefits that outweigh some wasted stats. For example, Lich Bane on Akali.