Coxeter groups are fun. I took it as a graduate course, but honestly you can get pretty far (and we did) just using elementary proof techniques that a 1st or 2nd year undergrad could handle.
Understanding Lie groups and differential equations is my current life goal, but I only took math up to linear algebra and differential equations for scientists and engineers in undergrad.
Also, as with a lot of places where algebra meets geometry, the 'homogenising' (in a good sense) effect of the algebra makes the geometry much less challenging than it could otherwise be. (Linear algebraic groups, which are a particular kind of scheme, underlie much of my research; but I understand way less about schemes in general than about the geometric structure of LAG's.) That's just to say that, from my point of view (as, admittedly, an algebraist), getting the solid linear-algebra background to handle Lie algebras as abstract structures is way more important to understanding Lie groups than a full picture of all the subtleties of differential geometry.
(With that said, anyone who wants to understand the geometry of differential equations will need at some point to handle a lot of non-homogeneous geometry, so my advice isn't the end of the story even for those who agree with it.)
I would recommend the book by Michael Davis for an in-depth dive: https://people.math.osu.edu/davis.12/davisbook.pdf