For filtering you can use a Chinois: https://www.amazon.com/New-Star-Foodservice-42566-Perforations/dp/B00GBG8MCA

They are common. You should be able to get them in an commercial food supply place or online. The wood thing is used to help squeeze more liquids out. They are also offered in multiple levels of filtering - rough (probably best for initially straining the botanicals), medium, and fine - best for clearing it up before a coffee filter or other filter.

For the storage you can upgrade to a fusti: https://www.amazon.com/Stainless-SPIGOT-Strong-Sealed-Gallon/dp/B07K4Q9F56

They have many sizes - from 2 liters up to 100+. It more expensive then plastic. It won't hold flavors/smells.