Hi Megan,
You might want to check out my Insight's Post on
Becoming a Medical Physicist. (Oops Ygggdrasil linked it while I was writing.)
Yes the best route is to start out with an undergraduate degree in physics. Some closely related disciplines can also get you in (engineering physics, biomedical engineering, nuclear engineering would usually also be considered), but an undergraduate degree in physics is typically what admissions committees in medical physics graduate programs are looking for.
From there you need at minimum an MSc and then a residency. It's becoming more common for students to complete a full PhD these days. There's also the "doctor of medical physics," or DMP option. And another route is to do a PhD in another field and then do a post PhD certificate and then a residency. If your goal is to do medical physics though, I would recommend aiming for a PhD right now.
Most PhDs in medical physics end up as clinical or hybrid clinical-academic physicists. Most MScs (and DMPs I believe) end up clinical. There are a few pure academics, but they're competing with all the other PhDs out there and the pay tends not to be as good.
For rough timescales:
undergrad: 4 years (you pay)
MSc: 2 years (some are supported financially, most are not)
PhD: 4-6 years (a few more offer financial support, TA or clinical physics assistant work as support)
DMP: 4 years (includes residency - unpaid)
Residency: 2-3 years (pay is similar to a typical post-doc)