Which train tickets do I need for a daily commute between Frankfurt and Heidelberg?

This is a somewhat unusual (and long) commute, so it's not covered by any of the local transportation networks (Nahverkehr) and you will need a regular train ticket from the Bundesbahn www.bahn.de

These typically only cover the actual train ride, so if there is also local transport involved (bus, S-bahn, subway) you may have to buy this extra.

As a student you can get a Semesterticket. This is tied to your place of study and not to your place of residence, so it would come from Heidelberg can cover the VRN area https://www.vrn.de/tickets/tarifsystem/wabensystem/index.html It covers "slow" regional trains (RE, RB und S-Bahn) but not fast trains (IC or ICE).

The Bahn offers a "volume" discount though it' Bahncard program https://www.bahn.com/en/view/offers/bahncard/bahncard.shtml. A one way from Frankfurt to Heidelberg will run you about 20 Euro without a card and goes down to 15 and 10 and 0 depending on Bahncard level

Depending on where your exact locations and how often you are planning on going, it's probably best to game out a few scenarios and see which ones work out the best. My hunch is that taking the Semesterticket in conjunction with a Bahncard 50 or Banhcard 25 will probably work best.

The winter semester has around 15 weeks, that's 75 days or 150 round trips. So you are looking at around 3000 Euro in train tickets. Spending 255 Euro on a Bahncard 50 knocks this down to about half of it, so that seems like a worthwhile Investment. If you have the Semesterticket, you would only need the train ticket for that part of the journey that's in Hessen and the Semester ticket would cover the rest. But that only works if you stick to slow train in the VRN area.

Another option would be to take a monthly ticket from the RMV that covers all of Hessen (up to Biblis or Gernsheim, I think) and then use the Semesterticket for the parts in Baden-Württemberg. Again, making a spreadsheet with a few scenarios would help with that.