Is this a reasonable thing to do, to improve their looks, or will they ultimately peel and look even worse? If reasonable, what type of primer is best?
I cannot answer the first part without seeing it but here is a good primer if needed
Here is a link that might be useful: primer
No matter what kind of primer is used the oxidation level of the aluminum is important. Consider a naval jelly if it is not satin finish or similar or pitted/oxidized at all.
A good oil based metal primer should be OK. You may have some trouble finding one that will say "for use on aluminum" on the label.
Airplanes are primed with Zinc Chromate but I don't think you can buy that just anywhere.