Which is better for the environment?

Without a doubt use the reusable containers and when using the dishwasher make sure it is a full load.

you can compost in an apartment setting. Look at books like Worms Eat My Garbage, and do a web search for Vermicompost and Apartment Composting. Most waste water plants use their sludge to fertilize city, state, and national park land, or sell it to farmers to use to fertilize their fields. So it's composted, but it's mixed with all the nasty toxic gunk people throw down the drain, like battery acid and prescription drugs and motor oil, not to mention good old fashioned raw sewage.

Those little baggies are washable, as long as they don't have raw meat or mold or anything else gross in them. Dry them on chopsticks or wooden spoons to hold them open in the drainer.

Your dishwasher probably has energy saving features. For most loads, you don't need to use the long wash, pot scrubber, or high-temp wash, or heat dry settings. Use them.

using a reusable bag and containers will save you money, too. For the price of 250 paper bags, and 750 plastic baggies, you'll be able to buy a nice lunch set that will last you at least a year, and probably longer.

creating more small plastic throw away sandwich bags uses more chemicals and pollutants than washing a reusable container.

If you ask around you may be able to find someone who does compost. You could save your compostables in the freezer and give them away once a week.

Using the reusable containers as when they worn out you can recycle them.

Why are you using a dishwasher go to the creek make a fire and heat the water and wash them out with sand.