Thanks a ton for the reply. I attached another picture with labels. No spa or anything. I have a total of 5 jets or outflows on the side of the pool. I'm not sure where they branch out since the equipment is around the corner from the pool, but one outflow from the filter. I neglected to mention the vac port, but currently it is shut off as I don't have an auto vac. Currently chlorinating with tablets in the skimmer basket, but open to any better methods if there is one!
OK makes total sense now that you labelled it. The single return pipe from the filter will branch off underground to each return nozzle in the pool. Great that you have 5 return nozzles. So a new filter and a VS pump would do well. You can program the VS pump directly on the display screen since you do not have automation.
If you want to follow TFP methodology then it would be suggested to stop using pucks. It is a completely different process from what a pool store will tell you. Also, you would need to buy yourself a test kit and that will help you understand the chemistry of pool water. Right now, as a minimum I would buy a floater and put the pucks in there rather than in your skimmer basket. You do not want fully diluted chemicals flowing to your pump and filter, especially if you are buying new equipment.
The concern with the use of pucks is that each puck adds chlorine, CYA and acid to your pool. To demonstrate this, each fully dissolved 8 ounce trichlor tablet (puck) will add 5.5 FC, add 3.3 CYA and drop pH by 0.29 in a 10,000 gal pool. The free chlorine (FC) is good. CYA is good to a certain level then it becomes too high and causes you to add even more chlorine to keep your pool sanitized. Whereas chlorine dissipates due to sun and attacking bacteria in the pool, CYA continues to accumulate until it gets to a point where the only option is to drain the pool and start fresh again. The acid in the puck is good to a certain point but in addition to dropping your pH it also drops Alkalinity. Then you must add chemicals to raise either pH or TA (total alkalinity) or both to maintain suitable levels. As Marty noted in his post - read the information.
If you elect to follow the methodology then the first step would be to stop using pucks and start with liquid chlorine. This is much more manageable for your pool but a little more work for you. Ideally you would install a saltwater chlorine generator (SWCG) to make life easier. It would be best to do that when you put in the new filter and pump. That way it can be plumbed properly and also electrically (the SWCG must only run when the pump is running).
Here is another link with a lot more info to read if you wish to follow the TFP methodology
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I know this is a lot to digest so feel free to come back with questions if needed.