I have sown three traays of sweet peas, of which about 45% have just about germinated in 5 weeks. Braod beans in deep rooting pots are about 50%, and loads of other Sweet Pea seeds are just dormant under a shallow layer of Vermiculite. I find that Vermiculite is as helpful as vermicelli ! Utterly pointless, kills off any germination, and the soil turns green underneath. On the other hand, this could be due to overly enthusiastic watering ! Probably this is the cause.
Generally, I have found that for a veg patch, sow seeds where you want them to grow, but, brassicas in a seed bed. Carrots, out in the garden, under a cold frame that will cover a small and short rowed patch. Beetroot, where you want to grow them , and in a well conditioned soil. I don't worry too much about the 'fertilizer' stuff in the soil, but heap a load of manure for the 'conditioning of the soil. The more veg matter in the soil, the better. Fertility ain't the 'b' all and end all. Condition is the primary thing. The rest will look after itself.
Get a good compost heap going, and wee on it as often as you are in the garden! Better than Garotta, which is the same thing, but ours is better ! Bring your friends around for a few bers sometimes, and watch your garden grow !