If you join Amazon Prime for their trial period, you get free 2-day shipping. If you decide you don't want to keep the Amazon Prime, you can cancel before 30 days have passed and owe nothing. Just a thought. (I joined it and sometimes when I order stuff it doesn't even take two days. Several times now I have ordered one day and gotten delivery the next.)

Using trichlor takes awhile to build up a CYA level so is not an ideal way to add CYA initially. You can just use bleach and add CYA outright if you want to. That is what I always do. I'm not familiar with the Home Depot pool products so can't comment on them.