Should I chill my milk?

Absolutely. Unless you drink it right from the teet, then the protein and nutrients in it that make it good for you also make it excellent for microbes to grow in (=culture medium). You need to keep it refrigerated for your own health. If you want to let it warm before drinking, that is ok. Not sure how you mean this question...
No. It is unnecessary to keep your milk at any colder temperature than refrigerated if you are planning to use it. Freeze your milk for storage up to 3 months in the coldest section.