The idea of raising animals in zero G for protein is, as some pointed out, a rather daunting task. If we were to go that route it'd likely have to be smaller animals that take up less space/use less resources. Crickets as some have mentioned or other insects would be a good choice there, beyond that my next suggestion would be a bird such as a chicken to provide an egg supply.
As for using plants and/or mushrooms. They provide problems of many of the plant based solutions for protein provoking common allergic responses to some people. So we'd need to make sure there was a decent selection to choose from eventually. That said, they are some of the better options since they could also help keep the CO2 levels down. I don't know enough about mushrooms to be able to advocate for or against them, but I do feel that they are more likely to be able to handle some of the issues of space than plants can.
Next on the suggestion of GMOs, I personally think those would be perfect, if not necessary, for space and for future colonies beyond Earth. Most GMOs given to the public are tested thoroughly to be as safe as possible, at least as much as any other food we consume if not moreso. Furthermore, they may be able to be modified to not only survive better in microgravity, but also to provide a boost to nutrition. I certainly wouldn't dismiss the need to continue studying them at the very least. The more we study and practice genetic modification, the better we'll be at it and the safer it will become as well.
Finally, it's quite the feat to make a fully self sustaining space station, but alas, on their own they'd never be able to have enough continuous resources to keep up the agricultural needs. Space stations will likely always need resupplies from planetside. They may be able to stay sustained for a while, but even when recycling waste there's a slow decline in what can be produced without fresh resources. I foresee symbiotic relationships between space stations and their planets. The planets provide the agricultural requirements while the stations provide satellite services, satellite maintenance, heavy industry work, and possibly even energy collection that can be sent down to the planet.