Math and economics have a few core upper level courses, but are broad enough that different schools’ departments may have different elective selection. In smaller math departments (like at many LACs), the elective selection could be limited, based on the interests of the faculty. Upper level math courses are commonly small. For a math major, depending on post-graduation goals (PhD program / research, finance / actuarial, high school math teacher, etc.), the electives to look for could be different.
Economics can vary in math intensity at different schools (either universities or LACs). The math prerequisites to intermediate microeconomics can give an idea of how math intensive a given department is (high: multivariable calculus; medium: single variable calculus; low: no calculus). The student who likes math may prefer a more math intensive department. Economics tends to be a popular major, so it may have larger departments with more faculty, but often larger class sizes.
Physics has a well defined set of core upper level courses. However, it is often a small major, so departments may be small, and faculty may be consumed teaching service courses to other majors and pre-meds. Check that the core upper level courses are offered with reasonable frequency.
As far as transferring goes, if he wants to transfer at the sophomore level, both college record and high school record / test scores will be important. If he wants to transfer at the junior level, college record will be the most important factor, while high school record / test scores will be less important.