Great plan. A few things, be sure the teacher is a bass instructor not a guitar teacher doing bass on the side.
When testing basses stick with one amplifier, and testing amplifiers stick with one bass. Test with any EQ set flat to minimize coloring the sound. Reduces variation that way.
On active basses when comparing to a passive one be sure to set the EQ flat. As an example the MusicMan basses have a spot in the center of the rotation of the EQ knobs that is "flat" where a passive bass you keep the knobs all the way up. Then they are on equal footing.
For a starter amp I'd go with at the minimum a 10" speaker ala the Peavey Minx ($85-$100 on E-bay). In their line up it was replaced by then Max 110 ($150). A 10" or 12" gives a better sound than a 15".
Avoid effects at first. They tend to hide sloppy technique. The most brutal thing is a headphone amp. You can't hide anything there.
Jim