We do a little of everything. If you buy the lunchmeat in the plastic container, you get a free container. Use it til they break it. We got a set of plastic containers at IKEA and are still using them a year later. I'm starting to lose track of some of the little lids, but so far so good. I also got some glad or off brand round containers - good for fruit and cut veg. If it comes back, horray! If not, well, um. Hope she remembered to hit a trash can. I put our little containers in the top rack. They turn out OK.
I also use sandwich baggies when I need space. Can't get it all in? Put the lunchmeat in a snack sized baggie (my DD eats deconstructed sandwiches) and shove it next to the freezer pack.
DD gets what she'll eat, even if it's the same cheese stick, fruit, ham, and tortilla every.single.day.
My DD has the the same Yubo box she'll use again in the fall. My biggest problem with that is that someone other than me put the faceplates in the dishwasher and they peeled. She is unexpectedly getting new faceplaces (but not lids). The rest of the thing is DW safe.
One day she may do like her sibs and brown bag it but for now, we're using the reusable daily lunchbox.