Although somewhat dated these days, the book Clownfishes by Joyce D. Wilkerson is a good source of information. For some reason folks are asking outrageous prices on Amazon, but I found a link where it's available for much less.
http://www.aquariumsupplycompany.com...65/3558742.htm
Baby brine shrimp, believe it or not, are going to be too large for the larvae for the first week. You definitely need roitifers for initial feeding. This means keeping phyto to feed the rotifers. Keeping phyto culture going & raising rotifers is not rocket science, but it's not that uncommon for your phyto culture to crash & then your rotifers starve. May take a few attempts until you get that process right. Upon hatching, the critters are considered larvae. They go through metamorphosis after about a week or so & it's only then that you can see that they are mini clownfish. Quite a few are lost in the first few days/week & many more don't survive the metamorphosis.
Lighting doesn't need to be anything special, just enough so the larvae/fry can see the rotifers. Water movement should be kept to a minimum since the larvae are tiny. I don't think a filter is used either, since larvae will get caught in that. It means daily water changes in some cases, & a lot of siphoning detritus & crud from the tank, again, probably daily. Rotifers & phyto need to be kept going as well, you guessed it, a daily chore. So probably not that much cost wise once you're set up, but a lot of time for the first few weeks/months until they are weaned on to dry food.
Good luck. Sicklid in Kamloops has a set up for breeding that puts anything else I've seen to shame. He's not on here much, but if you pm him, he can give you some pointers.