What kind of containers for homemade ice cream?
Restaurants solve this problem one of two ways:


Tough, professional-grade stainless or Lexan containers.  I suggest 4" to 6" deep 1/6 size hotel pans AKA steam table inserts, or lidded 2-4 quart Cambro containers.  
Cheap, disposable quart delitainers.  These are actually reusable and dishwasher/microwave safe, but at $0.25-0.50 apiece, it doesn't matter if they break regularly!  Just remember to recycle the broken ones. You've probably seen these used for take-out soups in Chinese restaurants or delis, because they're cheap but work well.  


For the first option, remember that professional-grade equipment is built to survive YEARS of punishing abuse, but you'll pay more for that quality.  Expect a pricetag of $5-7 or more for each of the smaller containers, or slightly less if you find a good restaurant supply store.  Sam's Club also carries some of that stuff.   

The flipside is that you shouldn't ever have to replace the containers unless you do something really dumb, such as putting a pan hot off the stove down on the lid. For this reason I suggest planning ahead before making a purchase, because you want to get the right sizes for regular use.