I'd love to see how far you have got - I had more of an interest in lambda calculus (and particularly combinators) but I have now developed a serious fascination with TMs. And yes the CS course I did covered them - but that was a long time ago!
https://www.youtube.com/watch?v=kmAc1nDizu0
Also the BB Challenge site - where I've been getting definitions of TMs to run:
e.g.
1RB0LD_1RC0RF_1LC1LA_0LE1RZ_1LF0RB_0RC0RE
I've ran that one even though there is no hope of me ever seeing it terminate
https://bbchallenge.org/1RB0LD_1RC0RF_1LC1LA_0LE1RZ_1LF0RB_0...