Feed primarily for good health, keep your water clean, and keep your fish from being stressed and the color will be there (assuming decent genetics as mentioned above).
With a nutritionally sound pellet there's no compelling nutritional need to vary the diet, because a good pellet would be nutritionally complete due to the variety of nutrients and ingredients already in the pellet. People sometimes confuse sufficient and balanced quantities of the various important nutrients as meaning a variety of products, but one doesn't always equal the other. Doesn't mean you can't add treats or use some variety if that's your preference, just means it's not required if your staple food is a balanced food.
Feed mostly mealworms and/or bloodworms or something similar and then you would want to vary the diet-- because these foods are nutritionally limited and incomplete. I've used mealworms in the past to get a fish started eating that was refusing to eat. I've found that freeze dried bloodworms seem to encourage some SA species to spawn more often. So, it's not that I'm against those foods, but they won't do much for color compared to a quality pellet, or compared to krill, some types of shrimp, some types of algae, etc.
As far as carotene relationship with color, some people have simplistic ideas about all of that. For one thing, beta carotene is only one of a fairly large family of pigmented nutrients of varying colors (carotenoids) that can be further broken down into sub-families, and beta carotene is certainly not the only important one, and not necessarily the most important for fish health or fish color.
For another, it's not as simple as red/orange nutrients in the food equals red/orange fish or since spirulina is blue-green it's mainly good for blue fish. Spirulina actually has quite a buffet of carotenoids, of colors that include brown, more than one yellow, more than one red/orange, etc. In other words, it's not as simple as carotene is red/orange, so it's good for red/orange fish and spirulina is blue green, so it's good for blue fish. What it is about is overall health and nutrition. You could overload a fish on synthetic beta carotene as part of an otherwise poor and unbalanced diet and get a very red or orange-- and unhealthy-- fish.
Pigmented nutrients can directly color the animal, the red/pink in salmon comes largely from astaxanthin; in fact, probably most red/pink aquatic organisms are rich in astaxanthin. But in some fish or invertabrates, astaxanthin can produce or enhance blue or purple, depends how it's processed nutritionally and how it's bound to other proteins in shells, feathers, scales, etc. And for the most part it's overall good nutrition (and good water) and the health benefits of more than one carotenoid that helps your fish color up and look healthy.
