When looking at courses, cosmology can come under a number of different titles. "Cosmology", "Astrophysics" and "Astronomy" are often used interchangeably, and although they technically refer to slightly different subfields, what you'll study is largely the same. You'll also find much of the basic core physics is shared with pure physics courses - it's also worth considering doing a normal physics course with options to specialise into astrophysics and cosmology later on.
Personally, I took a "Physics with Astrophysics" course, and that gave me flexibility that when I found the physics of stellar hydro/thermodynamics becoming too abstract and difficult for myself, I could easily re-specialise into a different area of physics (I've ended up in nuclear and radiation physics now).
If you want to stay in Astrophysics/Cosmology long term, the normal route overall is to stay in academia as a research scientist the whole time. You'll do some kind of physics/astronomy/cosmology course at undergraduate level, then continue to a PhD (possibly via a Master's course depending on admissions processes). After your PhD research, you'll stay on at University in a postdoctoral research positions, with many people eventually hoping to take up lecturing and professorial positions while continuing research.
I hope this helps! Good Luck
Best of luck in your adventures into Cosmetology!