A plastic grocery bag of course, can be used forever, but a zip lock bag for contacting the food directly should be used for too many times for hygiene reason.
I definitely reuse zip loc bags for storing food but won't go too many times
Here most plastic grocery bags are now dis-integrating rather quickly (yeah, ask me how I know).
whether or not your plastic container is rigid or not, it all depends on how you wash/clean/sanitize it.
If you are just talking hygiene, plastic grocery bag/zip lock/rigid or soft. They are all plastic. Plastic does and will absorb oils.
If you could specify EXACTLY what you are using your bags for and what you want from those bags, we would not have to play a guessing game to the answers you seem to be searching for.
For instance:
are you storing these bags in the fridge? or the freezer? or the cupboard?
are the items liquid? solids? ex: milk/sauces - hard cheese/soft cheese?
are they to be stored overnight? for days? weeks? months?
an example of overnight - sandwiches to take for lunch the next day.