If I were you, I just do a big water change to bring the nitrate down. Unless you have a chronic problem with nitrate and phosphate, I would not use these chemicals and resins. A 10% weekly water change or 20% biweekly water change will keep the small tank healthy and looking good. It's probably cheaper than using these chemicals, too. It's easy to mix and change one to two gallons of water every week or every other week, too.
Purigen, Chemi-pure and activated carbon take care of pretty much the same things - they adsorb dissolved organic compounds. Purigen is a type of resin and Chemi-pure is activated carbon with some deionizing resins.
Phos-zorb and Phosguard are both alumina based phosphate removers. They bind phosphate well, but Dr. Randy Holmes Farley reported a possible adverse effect on leathers.
Since your tank does not look plagued with cyano or any nuisance algae at the moment, I don't think you need any of the stuff you mentioned for now.
Tomoko