Some live food to consider:
White worms
Microworms
Daphnia
Mosquito Larvae
Brine shrimps
banana worms
I'm sure there are more much I have missed. Regarding the question about nutrients its really to do with what you feed to the culture. For example, things like brine shrimp will lose its nutritious value as they get older so what people tend to do is feed their brine shrimps with other food stuff such as spirilina and fish food etc prior to feeding their fish.
People culture different live foods for different needs, things like microworms are great for feeding fry such as betta fish fry as they have small mouths from personal experience I find small tetras will also love 'em. For growing out fish I have seen people use whiteworms, Daphina and Mosquito larvae, usually the larger type of live food. So it best to fidn out what you wan't to achieve then find out what food suits your need the most, not just its simplicity in culturing.
Which are most simple food to culture? It depends but personally I find Microworms easy to culture, I've never tried but Mosquito larvae sounds as simple as putting water in a bucket with dead leaves outside. There are a lot of vids on youtube which provide great details on culturing your own live food for fish.
Outside of livefood I often see people make their own food for feeding fish, these may include the use of vegetables like spinach and meat like beef heart or white fish and prawns. The great thing about making your own food overall be it live or DIY is that you know what your feeding the fish and its possible nutrient content. DIY fish food allows you to feed fish and observe which types of food stuff mix they prefer to eat and eventually you can tailor the food to the fishes' needs and wants.
Michael.