Definitely get a single strain as a starter. and getting them local (like from OGReef) is FAR superior.
Do you have the setup already or not? Couldn't tell between a few of your posts. I would familiarize yourself with a couple setups and ways to grow - some people grow batches, some people grow continuous cultures, and a few crazy people do chemostats / bioreactors. Each has a little different shopping list and pros/cons.
You can use 'fertilizer' - i'm assuming you mean like miracle grow or hydroponic fertilizer or whatever. Technically this can work, i've grown some on it in a pinch, but by far the most commonly used one is called F/2 or Guillard's F/2, typically bought in liquid form at a 1000x concentrate (so 1 mL per 1 L seawater). If you're on the fence about whether you can grow it or not, miracle grow can work, but since you need to get a single strain, you might as well pick up F/2 for another $10.
BTW Setups run the whole gamut - the best way to do it is like OGFrenchHorn does, check out his thread - glass bottles you can autoclave/bleach and acid-wash, round with rigid airline tubing to get even, strong flow, fully sterilize all seawater before inoculating. Basically treating it like the microbiology science that it is.
But you can also run it low tech, this is how I run it in the garage. Flexible airline in re-used bottles, clean Instant Ocean but not sterilized, with 0.5-1 mL F/2. Very janky but it works for me, and since I'm not selling i don't really worry about it being axenic (bacteria-free), just that no pests or coral-harmful bacteria pop in, and that's basically it. Full disclosure this is NOT the most repeatable way to do it, but if you have skills doing aseptic technique / growing microbes in some context, you probably have enough knowledge.