Chris,
New, Eden & Jubilee are all good courses & are worth playing a few times, but it is The Old course that is worth understanding deeply.
Don’t forget to consider, as time allows, to head south & play Elie, Leven, Lundin, both courses at Crail, & further south to play North Berwick, the courses at Gullane, Muirfield, Luffness New, Kilspindie, Dunbar, Craigielaw, etc.
There are so many interesting courses within a relatively easy drive from where you are that it would be a shame to miss the opportunity you have. That’s why I believe, in regards to The Trust courses, you should focus on TOC & then play as many of the other interesting courses within a 2 hour drive radius of St Andrews.
Gaining the best understanding of TOC, that you are able during your time there, will be something that you will value for years to come. So will playing as many interesting courses as you can.