Basically, "I'll put your tickets in the post today" is "I will send your tickets through the mail today. Referring to the mailing system as "the post" is more British. The sentence is a definite plan for today. Your other examples are correct as well, but they are not definite. You are planning to do something, but something might stop of from actually doing it. It might not happen. I hope this helps!

Your first guess is correct. The phrases about planning something are also all correct.