Welcome aboard!
You can start any time you'd like.
First, though, please post a full set of test results:
FC
CC
pH
TA
CH
CYA
These results will lead to the next step. You need your pH to be 7.2 before beginning the SLAM.
Once you have your CYA results, check out the
Chlorine/CYA Chart to determine your Shock FC.
Go to
PoolMath, enter the volume of your pool in the upper-left corner (orange bar). Based on your dimensions, I got 21100 as your volume. In the 'Now' column for FC, enter the current FC you tested. In the 'Target' FC column, enter the Shock FC from the Chlorine/CYA Chart. IME, picking a number slightly higher (1-2 ppm) than the Shock FC makes things go a bit faster.
From there, follow the directions in the SLAM article (posted previously by northrn).
I'm thinking you're going to go through more than 6 jugs of bleach in the first day...
Finally, brand names don't mean anything, so long as the concentration is the same. I found Great Value Concentrated bleach (unscented,
not "Easy Pour" or "Splashless") from Walmart to be $0.90 per jug (121 oz.) cheaper than Clorox. I used some 90+ jugs of bleach for my SLAM (mine was much worse than yours sounds), so that made an $81+ difference for me.
You've already made the right decision by coming to TFP. A little studying, some questions, and patience will get you there quicker (and cheaper...) than you might think.