Faster growing macroalgaes generally remove more nitrate and phosphate than slower growing macroalgaes. If you want to reduce nitrates and phosphates to keep up with the waste produced in the aquarium, then you pretty much will always want a fast growing macroalgae. Chaetomorpha is more an algae that you would want to use in a sump. It grows in clumps and isn't very pretty in a display tank. Kelp grows fast and can be pretty. Red Graselaria and caulerpa racemosa are also pretty fast growers. Any species of caulerpa is a good choice, other than toxifolia. Caulerpa has "runner roots", so harvesting that macroalgae is easier than others. All you have to do is pick up an end piece and it pulls up the rest. If you want to really make your tank look good like a display refugium, put long leaves of kelp in the back, caulerpa throughout the rockwork (different kinds) and perch some pink galaxy algae here and there for some additional color.
Algae, for me, is half the equation. Yes, algae can remove nitrates, phosphates, heavy metals, ammonia and some chemicals BUT, if you have a lot of fish in a tank you will also need an adequately sized protein skimmer and some mechanical filtration and carbon for sure....
Mechanical filtration and powerheads take care of all of the particulate organic matter in the system. Protein skimmers remove particulate and dissolved organic matter before it has a chance to break down into nitrates and phosphates and macroalgaes "mop up the rest." It's a pretty delicate balance.