I'm not a fan of the dedicated machines. They take a lot of space for a single purpose. I prefer the stick style sous vide devices. They are easy to store, and you have several choices for containers and sizes. Plus, the containers can be multipurpose use, like pots for cooking, or cambro containers you can also use for brining, food prep and storage.
You don't really need a cooler. An insulated container is not needed for the sous vide stick to maintain temperature. It won't struggle, and it's not like you are saving much $$ in electricity by using a cooler. Plus, now you have to store this giant cooler that now only serves a single purpose because you've cut a hole in it. Nothing wrong with repurposing a cooler you are going to throw away though. Not sure how styrofoam would do with higher temps. You can wrap a towel around your cambro container if you feel you need to, but it's not necessary. Here's a link to a
neoprene sleeve that might be a more elegant solution than a towel. I just use a cambro container for all sous vide, long and short. Just replenish the water loss every so often if you are doing a long cook for more than 12 hours... or buy a nifty lid to help minimize heat and water loss. I highly recommend buying the lid. Below is the cambro container and lid I use with my Anova.
Cambro 12 qt ContainerSame Cambro Container, different priceThis is the lid I haveAnother nice lid optionYou can also find a number of food-safe container/lid combos by Rubbermaid, Everie, Lipavi and probably others. Just make sure the lid is compatible with the container you choose (they are not interchangeable), and the lid is made for the brand of sous vide stick you choose.