College courses and grades.
However, if you want to transfer after one year (entering the new college as a sophomore), your high school record will matter much more than if you want to transfer after two years (entering the new college as a junior).
Also, at the most selective colleges, top-end college record (and high school record if applicable) are merely necessary, but not sufficient, to get admitted.
As a pre-med, if you are not a California resident and did not get one of the very few high-end scholarships at UCLA, you may want to consider retargeting your transfer goals to a less expensive college (e.g. the state universities in your state of residency) so that you can save money for expensive medical school. If you are a California resident, then UCLA has plenty of prestige that you seem to be seeking at a lower cost than the expensive private schools you mention.