Here's what I do.
First, lay your things out and have a close look at them, checking for any wear, pilling, holes or visible dirt/grime. You may or may not choose to repair – by simply replacing buttons or closures, darning or prettily embroidering around any holes, worn patches or unravelling seams and address the pilling in areas of high friction like under the arms, cuffs or back - by gently removing the pills.
I’d recommend either a wool comb or better yet, use a mains power electric (not battery) Clothes Shaver for a more gentle and consistent attention rather than just cutting off with scissors or blades and risking snipping into your hand knit or hand crochet.
The Classic 50 Clothes Shaver can be used on your family’s clothes, suits, woven and even upholstery fabrics too. It’s the tool of choice for many dry cleaners and fabric care specialists and unlike, the small wool comb, it won't get lost in the knitting bag. In fact, why not keep it with your iron?
Next, I’d get set up to hand wash on a fine day – not too sunny or windy - and just lightly launder using a gentle Eucalan delicate wash which is biodegradable and safe – not a harsh stripping detergent. Available in 4 subtle fragrances and unscented too. It’s a non rinse solution which is a time and water saver but my recommendation is to measure it out with a teaspoon (1 tsp to 4 litres of lukewarm water or less if you’re just washing a pair of socks or small item) into a basin.
To wash, just press the item below the water until it absorbs all the water. Gently squeeze the item to release any dirt and you can leave in that water for no longer than 10-15 minutes - about a cup of tea's duration - then remove from the water, drain the bulk of the water - I sit in a clean colander for a few minutes). Remove excess water by rolling in a clean towel and laying flat in the shade – ensure your garment lays in the shape it’s meant to and just allow to dry naturally.
Store in your preferred way. I'd avoid folding in half along the centre fronts and back to prevent permanent creases. If you want an expert tutorial on folding, why not see Marie Kondo and her special way of wrangling clothes. Link to her YouTube video here.
There are special purpose zipped or vacuum sealed bags that prevent insects getting into the fabrics. I don't use chemicals near the actual garments but have found that those moth traps kept in the wardrobe area help me keep a check on insect activity in the hot months. There will be a lot more advice as to keeping those woollies bug-free on the internet. Martha Stewart has some advice on protecting against clothes moths here.
However, I do have some very special knitwear that is stored in sealed bags in my deep freezer so that "No way! Never!" will any moths venture near them. It’s kinda cool hearing the kids say “Mum, where’s the ice-cream? and why's your cardigan in the freezer!"