I got my mom a Blue Yeti for teaching online classes and it's been pretty solid. I thought it was around $100, but looks like it's $120 on Amazon right now.
If you have a bit more budget, the Shure MV7 seems like a great option. One of my friends is an audio engineer, uses one of those and, at least, sounds pretty great over Discord :P.
I got the Fifine T683. It was one of the cheapest I could find that had a boom arm and a pop screen.
I personally recommend getting something with a boom arm. You can put the mic right up in front of your mouth and move it to sit comfortably. And it takes it off the table so it doesn’t pick up as much table noise.
Someday I might invest in a more expensive option but this was a huge upgrade for me in terms of quality. Beyond this it’s diminishing returns in terms of improvements vs cost. I think something like this is a good starter option.
A headset could probably work but I don’t have any experience with them.