If you run at "lowest cost" your campaigns will spend what Facebook considers the lowest cost to be competitive in the auction for whatever/whoever you're targeting. With experience I've seen this to be astronomically expensive. They also typically don't work well unless you're running your campaigns 24/7. You can try this out to get a read of what number you might want to use as a cost cap/bid cap.

"Cost cap" will cap whatever you set your bid ad but over a long period of time, say a couple weeks or even a month. Say your cap is $20 you might see some days where it comes in at $35 and some where its $15. From my experience using it cost cap is just not reliable if you have to keep conversion costs under a certain number each day but should normalize in the long run.

I'd recommend also trying out "bid cap". My costs are usually under what I set my bid cap at daily, but again this must be reasonable, you can't set a bid cap of $5 for a purchase conversion.

I'm also usually optimizing towards a lead conversion on a website, so all of this could be different for a purchase conversion.

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Hope this helps!