Wait until the rind is HARD- if you can pierce it with a fingernail, they're not ready yet.
Really, there is no hurry unless you've got mice getting into the garden patch. As far as "color changes"- some squash doesn't change color, at least in my experience! Butternut squash stays sort of tannish once it gets to it's full size, but it will still "ripen" a bit after that.
Around here, we don't pick it until frost threatens (or unless some disease kills the vines) and then we have a giant picking afternoon and clean out the garden of every possibly ripe or "close enough" veggie.
If you want to store them, wait until they are hard shelled, then pick by CUTTING THE STEM- don't pull them off the vine. If you break the stem off some, set those aside to be used up first- they won't keep long (a week or two, not months like if you don't break the skin).
Handle them gently- they're not peaches, but they're not footballs, either! SET them in the baskets, don't throw them! Wipe them off with a weak bleach solution, and then set them someplace warm (if possible- around here, by the time frost threatens, "warm" is usually only a dream) and let them "condition" for a few days. This helps harden the skins further and helps them keep for the winter.
Store them someplace DRY and cool- dry being even more important than cool. But not where they will freeze- instant rotten squash once they thaw. I've stored them for months in a cool bedroom (heat turned off), and currently store them in our basement, which runs between 50 and 60 °. But NOT in the root cellar, which is a bit too damp, and which encourages mold.
If at all possible (it's really important) don't store them piled in baskets or boxes- store them in single layers, preferably on a ventilated shelf. A regular wooden shelf is fine, though.
If you do all of the above, you may well be able to serve winter squash for Easter dinner! They may be a bit dry by then, but some may still be edible.
If you get some that are getting "bad spots" on them- starting to spoil, don't let them go to waste. Cut out the bad spot and cook the rest (easiest way is to remove the seeds and strings and nuke the thing until it's soft. Then scrape the edible flesh away from the skin. It sure beats trying to peel them raw!). Freeze it for later meals.
Summerthyme