Read this thread, it should answer all of your questions:
http://forums.studentdoctor.net/threads/elite-school-bias.1169892/
tl ; dr : School name is not as important as the rest of your package but certain schools are heads and shoulders above the rest in terms of sending students to MSTPs. Notably, school prestige seems to be more important to MSTPs than MD only programs
(Rank in terms of # of students sent to MSTPs) .....University......Number of students sent to MSTPs in 2015.
1 Harvard University ................................... 25
2 University of California-Los Angeles ....... 20
3 Cornell University .................................... 19
3 Yale University ......................................... 19
5 Massachusetts Institute of Technology ... 18
6 University of California-Berkeley ............. 17
7 Washington University in St. Louis ......... 16
8 Columbia University ................................. 13
8 Johns Hopkins University ....................... 13
8 University of Florida ................................ 13 ....... 173 ..............
28% of the class in the Top 10 UG Colleges (by volume)
11 Stanford University ................................. 12
12 University of Michigan-Ann Arbor ........ 11
12 University of Pennsylvania .................... 11
14 University of Chicago .............................. 10
14 University of Washington ....................... 10 ........ 227 .............
36% of the class in the Top 15 UG Colleges (by volume)
16 Duke University ...................................... 9
16 Princeton University ............................... 9
18 Northwestern University-Evanston ........ 8
18 University of Pittsburgh ......................... 8 ......... 261 .............
42% of the class in the Top 19 UG Colleges (by volume)
20 University of California-San Diego ............ 7
20 University of Illinois at Urbana-Champaign.. 7
20 University of Maryland-College Park ............ 7
20 University of Wisconsin-Madison ................ 7 .......... 289 ............
46% of the class in the Top 23 UG Colleges (by volume)
More general advice: It is way too early for you to decide if MD/PhD is for you. I don't care if you have been doing research for four years in high school, you
will change in college. Your priorities, your career goals, your personality, what you know, what you like - some of it or all of it will change. Leave room for that change and don't tunnel-vision any particular path. That being said, it's great that you are considering the dual degree and research and I would say Cal Tech is among the best if not
the best place to go to undergrad in order to become a scientist. Other schools to consider would be MIT, Berkeley, Stanford, Harvard, and Yale (that order is my personal preference, they are largely interchangeable in terms of prestige and research opportunities). If you are the type of student that gets into CalTech you will rise to the challenge of competition but it will not be easy at CalTech. It's not a cutthroat competitive environment from what my one (read n=1) friend at CT has told me but it is very, very hard to have an excellent academic record coming from there and your record will need to be nothing less than excellent (3.6+ at least, 3.8+ ideally).
My personal advice: Go to the best school that accepts you that you feel comfortable paying for. Go somewhere where you can get an education (one not solely predicated on professional school that emphasizes more than getting a job but can provide more substance than a latinate piece of paper).