This is an area where good heuristics solves most of the problem for you, and maybe all of it. Overthinking this is the enemy.
figuring out if each thing is worth selling, donating, or throwing away
You're already overthinking it. The objective here is to simplify your life, not to maximize your income from the shedding operation or find the most appropriate way to donate something. If that has a monetary cost in selling something too cheaply or donating something saleable, that's the cost of hoarding things you don't need.
First, look around you. If, for each thing you see, you can't immediately say why you have it, it goes on 'get rid of' list. This means you'll get rid of something you'll need later on, most likely. That's okay. Rebuying something will imprint in your mind why you need that thing.
Sell anything obviously saleable and big ticket. Couch, computer, bike.... anything that can go quickly on Craigslist for a chunk of cash to the first person who says "I'll take it". Price it to move, not to get rich. Remember the objective.
Donate the rest. Places like the Salvation Army will take a lot of different stuff, and you can just dump it on them. Googling your local recycling or donation centres will give you some more answers. Remember the objective.
Throw out the rest. Again, you'll likely find yourself throwing out a lot, and feeling bad about it. That's good, because the next time you're in a store trying to talk yourself into buying something, you'll think of that huge, wasteful purge, and wonder if this thing you're thinking of buying will be part of the next one. If it's not immediately obvious why you'll keep it around, don't buy it.
Go through a couple cycles like this, and you'll have a lot less stuff around, you'll know why you have the stuff you do, and you'll feel a lot less encumbered by possessions. Also, remember that this doesn't have to happen all at once. Every Saturday, find a bunch of things to donate or sell, and do it. Every Friday night, throw out several things you don't want. Eventually it becomes a continual, easy pruning process, which is ideal.