I have two favorites for storing leftovers:
1: a set of glass Pyrex in convenient sizes with snap lids.
2: durable plastic tubs that nest beautifully and have tight-fitting interchangeable lids.
Plastic deli storage containers:
I first discovered these handy plastic containers when my city banned styrofoam and my favorite thai place started using them for takeout. I think they're pretty standard use for restaurants.
They're durable, their lids fit super-tightly (and are interchangeable for all the different sizes), they stack for great space-saving in the cupboard, and they also stack well in the fridge.
*Note: I don't know which brands work the best. I've heard of some breaking (though I've never experienced that myself), so maybe looking for something that claims to be "freezer-safe" would be a good idea? I've ordered two different ones from Amazon over the years and they've all been great.
For most people, my advice would just be to recognize them and keep them when you order out, but if you're in a situation where you have greater needs, they can also be ordered online in 8oz, 16oz, and 32oz sizes.
Glass storage containers
(Wirecutter recommends a different 18 piece set of glass snapware made by Glasslock.)