28 Days is the canonical tutorial, but there's also absolute beginner and z80 heaven and don't forget about the official developer's guide and system routine reference. wiki ti has good references although not much in the way of tutorials.
Also don't worry about "breaking your calculator". Yes, if you make a mistake, your calculator will crash. But just pop a battery out and back in, you'll get a RAM clear and you're set to go. Just keep your work in the archive and there's nothing to worry about- you're not going to accidentally brick your calculator.
To directly answer your question, the best option would be to get Mimas onto your calculator by any means possible. It is an excellent on-calculator assembly IDE, and if you can download just that to your calculator, you'll be set. Without it, you'll have to program directly in hexadecimal (machine code). Don't let this scare you, although it is more tedious, it isn't any harder than assembly, like how assembly is harder than Ti-Basic. That's actually how I originally started learning assembly, translating the opcodes from tutorials into hex from the instruction set before I was able to download Mimas to my calculator.
Either way read through all the tutorials and try things out until stuff starts clicking. None of the tutorials are really that amazing to be honest, so don't be afraid to ask questions if you're having trouble, although I might suggest that you also cross post on other sites like cemetech which aren't focused on Ti-Basic, not to say that you won't find good help here