Those items like watches etc can be sold cos you don't need them. Go to any merchant, sell menu, and look at what each item is for. If used in crafting, can keep, if only for exchange for money, then can safely sell.
Can also sell away those mod chips that are green, and later also blue when you get more and more purple.
You can buy back some of those machine cores and glasses. There is one merchant in the main city specialising on machine parts. Go to Buy menu, in the item list, it will show an icon besides those that you currently own. Then go to Sell, and sell away those particular ones, cos you know you can buy them back. (You can sell at any merchant but this one lets you cross reference.) There are parts from some of the corrupted machines that cannot be bot back, so don't sell those.
You can also sell away all the animal parts (skin, bones). They are used mainly in crafting your inventory capacity. So after you upgraded all, don't need to keep them any more. They are easy to get farm back anyway.
From mid-game, when you have lots of money already, can ignore items for crafting potions (and probably traps and arrows), cos you will be buying them most of the time instead of crafting them on the fly.
But yeah it's tedious to get rid of rocks and sticks. Treasure chests also hard to get rid but recent patch lets you drop them.