If you want to keep minnows alive you need three things
1. Fresh Water
2. Oxygenated Water
3. Cool Water.
If you have these 3 elements minnows will keep a long time.
If you want to use an aquarium, place it in a cool, shady spot. Too much sun and heat will kill the minnows very fast. An aerator is a very good idea, in fact probably required to keep the minnows going more than just overnight. Adding fresh de-chlorinated water daily will help keep them going too. For your own tank, be sure to put something on the bottom, rock or gravel. Grab a bucketful from the lake next time you are out. Be sure to get gravel from the lake, the gravel is full of stuff that will reproduce in your tank and help provide food for the minnows. It also contains bacteria that will help bread down fish waste. Supplemental feeding with tiny fish food every couple of days is good too. Keeps them fat and lively!
I don't use an aquarium but keep minnows for weeks with maybe a 10 percent mortality. (unless i forget to take care of the minnows properly)
This is how I keep mine alive.
I buy several dozen at a time, when at the lake I drop the inner bucket (I use a frabill 2 section type bucket) into the lake, the minnows stay cool, eat planton or whatever they eat and have oxygenated water.
When i leave I put fresh water from the lake in the bucket. At home I have a fridge in my garage. I put the minnows in the fridge, set at around 40 degrees. If they are kept for more than a couple of days I take out about half the water and add fresh. You can use tap water, put it in an open jug for about 12 hours then add to the bucket. By letting the new water set out the chlorine disapates naturally and does not affect the fish.
Before you go to the lake with your refridgerated minnows I find its a good idea to let them sit out for about an hour. Otherwise they die of shock when placed on a hook and then dropped in water that is more than 5 - 10 degrees different from the water they were stored in.
Right now I have about a dozen minnows in my fridge from a bunch I bought at the beginning of the month.
Hope this helps
Dan