Start out by following the directions given by Kodak (and Formulary for TF-4). You can also find excellent papers on Kodak's website about how to develop film and process to high quality.
Regarding the chemicals in your picture, you don't seem to have a stop bath there. There are differing opinions on whether or not you need to use one, but if you don't, you'll need a proper water rinse after you pour out the developer and before you pour in the fixer.
TF-4 is an alkaline rapid fixer. I think when you're saying you read you don't need Photo-Flo with TF-4, what you really mean is you don't need a Hypo Clearing Agent with TF-4. Here is the background: After fixing, you need to thouroughly wash the film. Using a Hypo Clearing Agent after the fixer can reduce the washing time. It is said with an alkaline fixer like TF-4 (as opposed to most other rapid fixers which are acidic) the wash times will already be shorter than usual, meaning a Hypo Clearing Agent isn't needed to speed up washing. Having said all this, you don't need to use a Hypo Clearing Agent with film anyway. You just wash the film longer. Again, follow Kodak's directions (and the directions for TF-4).
Photo-flo is a wetting agent used after the final wash. It helps the film to dry more evenly and prevent drying spots.