So, apparently making texture packs is quite difficult. I was planning on starting with Spider Armor (thought it'd be relatively easy to just remove the limbs and tint it), and... I have no idea how it works at all.
Honestly, this is probably above me. I think we all just have to wait for somebody with actual talent.
As for concepts, I've got some ideas. For the Jungle Creeper (the jungle variant of spiders), it's pretty simple. Monkeys would fit pretty well. For Blood Creepers (the Crimson variant of spiders), we don't really need a theme. As long as it's gory and disgusting it'll work for the Crimson. Maybe some kind of worm? Although I doubt that's much better.
And then there's the normal spiders. A lot of the enemies in non-corrupted cavern areas seem to be skeleton variants (such as Skeletons; Tim; Undead Miners; Skeleton Archers; Armored Skeletons; and although not an enemy, a very clear example of this theme: the Skeleton Merchant). Maybe it could be some kind of skeleton that climbs? It could be the "Skeleton Hiker" or something? But yeah, probably just a black version of monkeys or something. Maybe the Black Recluse could be a gorilla to signify that it's stronger.
Sounds and item names cannot be changed, so honestly it mostly doesn't even matter. You can't have a monkey sprited enemy called "Black Recluse" which drops an item called a "Spider Fang".
If one were willing to use mods to modify these however, I propose that monkeys drop "Monkey Tails", which you can use to craft "Monkey Armor". <Tooltip: "Feels comfy."> The Spider Staff/Queen Spider Staff could be replaced by a monkey that throws bananas instead of spitting poison.
As for the mushroom biome, something like a fantasy tree seems like it'd fit, but I haven't really been able to come up with anything more than that. I really like the idea of an underground forest feel with some kind of special "moss grass" spreading. Maybe the enemies could be pixies now that those are introduced? Maybe they're native to this biome.
The Truffle could be some sort of Groot-looking thing. At first I thought of a witch doctor then I realized that the Witch Doctor exists, so a tree man would most likely fit.
The furniture could be really interesting with moss and vines growing all over them, but unlike the Jungle they could also have a "woody" feel to them.