I've not got tons of practical experience with a lot of these things myself, but I've done a fair bit of research myself, listening to various clips and such, so I'll just put up what I've noted, and some things I've read.
What factors contribute to the tone of a guitar (electric) and to what extent?
Long story short, I'd say everything contributes. The guitar is a physical instrument that causes sound by way of physical movement, so almost every thing that you alter will in some way have an effect on the way the instrument responds to vibration. Change the neck join? Change the wood? Add chambering? Everything (that isn't the electronics) changes the physical properties, and the way it responds to vibrations. And the when the electronics get changed, well that potentially colours the sound in various ways too. So the way I see it, every change to a guitar will alter the sound.
To what extent is a much more relevant question, though. Because while I said, for example that the electronics "potentially colour the sound", well if you're just replacing stock pots or switches with pricier ones, you probably won't hear a difference. Swapping out the pickups though will potentially make a guitar sound pretty much like a whole different guitar! Pop dual 'Buckers in a Strat and it won't sound anywhere near the same. But swap the neck wood from Maple to Mahogany and you probably won't notice a ton of difference. It will be there, it will be slight, but you'll have to side-by-side compare them to notice it. Heck I noticed more of a difference between a Hendrix Strat and a Standard Strat than I've noticed from plenty of other videos of tonewood comparisons.
Another thing to consider is everything after the guitar. Because ok, you'll be able to pick a difference if you side-by-side a Mahogany Strat with an Ash one, the more effects you add after the fact, the harder it is to be able to spot the differences. You ain't tellin' those Strats apart through the Korg Miku Pedal, that's for sure.
All things said, I think Pickups and Effects/Amplifiers have the biggest impact on tone out of everything, and most other factors can be easily compensated for with a change in Pups, amplifier or effects. Other things should be chosen based on what you like the feel of, or the look of. Rosewood is a little nicer sounding to my ears on Strats, but gosh darn a gloss Maple fretboard just feels SO MUCH BETTER!!
What kind of wood produces the best kind of sound for an acoustic?
Well to be frank, I don't like this question, as the "best sound" is always a subjective thing. I believe though, if we're looking for a general consensus, Mahogany back, sides and neck, Spruce soundboard, and Rosewood fretboard. However personally, I think my own acoustic that I bought is one of the best sounding acoustics I've ever heard, and it's basically just QLD Maple instead of Mahogany, so if I was gonna make a personal call, I'd say that's my idea of the best sound. But do note that I'm not well versed with Acoustics, so I've not got as much to add because of that. But I do know that the woods on an acoustic make a MUCH bigger difference than they do with electrics, as they resonate much much more.
Does wood effect the sound of an electric guitar?
Yes. Though not to as great of a degree as pickups, effects and amplifiers.
Any suggestions on wood types?
I'm not sure what you mean by this at all What do you mean here? Like woods we like? Weird woods that are cool?