it really doesn't matter much. if your substrate has good drainage qualities it'll be fine. 30% perlite with coco and 50% perlite with sphagnum peat moss base or high water capacity soil etc. Perlite can be swapped with any number of options. Vermiculite adds some silica. you don't want anythign too chunky and large that roots have to put in great effort to get around it. so large wood chips are a bad idea etc. extra chunky perlite is bad. larger clay pebbles aren't so great. but they all work.
this also allows excellent o2 penetration which is good for roots.
when i germinate a seed, i use a simple small solo cup container. anything small is good. It should match size of plant, which will be tiny. It should be relatively fluffy substrate, not compacted.
I do wet this first. This is to avoid the chance that teh irrigation pushes the seed deeper into substrate than initially planted. i press a finger down about 1/2" or 1cm. this forms a fairly stable basin even if the substrate is very fluffy (a good thing). this will hold the seed. then i loosely cover and gently tamp down.
the depth you bury it wil impact how long it takes to sprout. Speed is great, but if too fast it won't pull off the seed shell. it's better the substrate pulls it off than any home surgery. adjust depth so that you get the fastest sprout time but rarely have to pull off a seed shell.
let it develop some roots before transplanting to your pot.
how often do you water? you water when the top layer dries -- superficial layer with coco, but 1/2 to 1" deep in higher water capacity soils. You water entire volume. this is why it is important the pot size matches plant size. otherwise the pot is sopping wet for 10+ days and just going to grow a bunch of weird shit in there. a good wet-dry cycle that isn't so extended in time is much safer and healthier for the plant.
so get the whole thing wet. no dry pockets! wait for top layer to dry and repeat. never give partial irrigations. dry pockets lead to buildup of nutes and unsafe conditions for roots and plant.
as far as watering before or after a transplant... i'd always water after a transplant. it helps settle the substrate - may see you need to add a bit more on top, in fact, if it settles in too much.
if soilless get a 10% runoff waste each time, religiously. if soil, try to minimize runoff while still saturating entire pot. you can learn this retroactively as you learn how much it needs. you don't choose a volume. you give what is needed to get the whole thing wet. if you re-irrigate at same loss of weight, it'll require same volume of water as before. you'll only need runoff in soil if you mistakenly feed too much in addition to what came amended in the soil.