Big fan of Gracilaria in particular. It is my preferred macroalgae for my refugium as it is easy to remove, doesn't get full of gunk, and has thicker growth making flow a bit easier to figure out.
I get good results with the following:
1. Good flow is paramount. I notice insane growth rates with increased circulation. I have a maxi jet pump in there keeping the water moving. If your flow is insufficient the algae will choke itself out and get clogged with crap, and nutrients will not reach enough of the algae.
2. Natural sunlight color temperature is more than sufficient, but reef tank lighting works well too. IMHO for some algae we overthink spectrum. These organisms have been around hundreds of millions of years. They're not going to go "myeahhh,no" if the light is slightly blue or red, but a simple grow light with good intensity does great. Since the algae is red, that means it's reflecting red light the most so I would probably steer clear of red. The brightness of your lighting will determine growth rate.
3. Detectable nitrates. Phosphates are less important, but Gracilaria is cultured on large scale in areas where water has detectable nutrients.
4. Studies show pH has a correlation with growth. The closer to 8.0, the better. Below 7 it will start to die off. Brighter lighting will help with that. More photosynthesis = more consumption of CO2 = higher pH.
5. Supplementation with iron/potassium. Gracilaria is nutritionally dense and contains high amounts of iron, calcium, and potassium. A small amount of iron supplement anecdotally boosted growth for me. I don't go out of my way to add too much potassium, but it's likely the algae is taking up whatever I dose as well.
6. Periodic thinning. Gracilaria has separate, free-living sporophyte and gametophyte stages. Periodic thinning helps sustain growth and prevents culture crash from spores. About once every two weeks I take about half of it out.