I recently saw a Plants & Flowers of Maine Facebook post that asked about fall cleanup which had a variety of ideas about what to do. Some folks were adamant about doing it their way, but I feel there's no strictly right way to do it. If you have plenty of time available in the spring, you can wait till then. I would probably advise cutting back any foliage on plants that are diseased however, (discard them in the trash) and if you have a mouse or vole problem as I do, removing the seasons foliage keeps mice from building nests in it, and seems to make voles apprehensive about exposing themselves in the open garden.
I have so much to do in the spring, what with digging and potting over 10,000 plants, replanting, etc.,etc., that I have to do a total cleanup in the fall. I like to wait until we have a frost or two, and the foliage on most plants has turned yellow or brown- this fall with our extremely warm weather and no frosts as of October 11 (never seen that happen), I'm having to cut stuff back while still green.
I start with Hostas and Daylilies, as their foliage gets soft and hard to cut as the season progresses. Then I go to plants that are showing the least amount of green, and go on from there. Everything goes into the compost pile- if you can make it big enough, it will soon become active and hot- just what you want.
Some folks on that P&F of Maine Facebook page suggested leaving everything for helpful insects, pollinators and birds, and I commend them for their beliefs. I've been an insect, pollinator, bird and other creatures aficionado for over 60 years. I have been cutting back foliage from my gardens since I've been in business- 35 years, and I have more different pollinators than ever- many species of flies, bees, wasps, hornets, butterflies, moths, beetles and true bugs. (I grow over 300 varieties of perennials, perhaps that's why so many pollinators.) Native beneficial insects are plentiful- ladybugs, lacewings, mantids, dragonflies, yellow jackets, ground beetles and more. I also have very few plant pests, Heliopsis and Asclepias aphids the worst.
I also have a pretty decent variety of birds that live and work in and around my gardens. I like to leave seeded perennials as long as possible, but I'm fortunate to have fields and woods surrounding my place for birds and other creatures to find food.