There are glass, cast iron, and ceramic teapots that come to mind, and if you aren't looking for handmade or intricate, 100€ is likely more than enough. Are you looking for gong fu style or European style?

I've never been disappointed by a glass teapot with a metal infuser.

I also never use lids, so I wouldn't think there was a problem with your first teapot 😄

Might be too late by now, but I have a mono filio and it works well. It's one of two glass teapots(which I know of) that are 100% plastic free while also having a large infuser basket. The other one is the Bodum Chambord(specifically the glass-and-stainless-steel version), which might be even better because of how the basket is constructed(that is, it might let fewer little bits pass through), but I don't have any personal experience to confirm or deny that. As far as I know, either one would just fit into your budget.

And yeah, I know that if you ignore the size of their filter/infuser baskets, there are plenty of other plastic-free glass teapots. But my recommendation would be to get one with a large infuser basket, and afaik that's only those two.

I am a big fan of Zero Japan's teapots. Glazed ceramic, and i have put them in the dishwasher for years with no issues. I think they also go by the name Bee House. The infuser they come with is pretty good, but it turns our that the mouth is also the perfect size for a Finum medium basket strainer.

This was my first result with a Google search.

https://www.teabloom.com/teaware/glass-blooming-teapot.html