Just my experience....I do not have any teacher's menu.
I started with multiplying 2
( I reviewed adding by doubles first) such as 2+2, 3+3' 4+4' 5+5
Then multiplying 10, so they know what multiplication is, also they think it is not so hard.
Then multiplying 5
They always end with 0 or 5
Then multiplying 9
Using the finger tricks
I made worksheets for thoses numbers that my kids usually forgot.
I didn't have a system to teach the table. I started with the easiest first. I think 6. 7. 8 are the hardest so I taught them in the end.
Then we practice while we are driving, we only learned one number a time and we kept repeating it. Hope this helps.