If engineering is the primary interest, consider small engineering focused schools. SD, NM, CO, MO, and a few other states have public schools of this type. There are also various small private engineering focused schools like IIT, RHIT, MSOE, WPI, Caltech, Harvey Mudd, Stevens, Kettering, etc… Harvey Mudd is also considered a LAC.
3+2 programs seems to be well marketed, but consider the hurdles that often prevent transfer to the “2” school: cost of an extra year, not knowing FA at the “2” school, not getting admitted to the “2” school as a transfer. So if engineering is a strong interest, it is best to choose a college where it is available natively.
Physics has a fairly well defined set of core courses for the major. Check that they all exist and are offered frequently enough (statistical / thermal physics is often the one offered least frequently). Bigger physics departments may offer additional electives.
Math is a broad subject with many subareas. Take a look at the catalog of a college with a big math department, then compare the offerings of the smaller schools of interest to see what they cover.