Try them in about 25~30% sand+25~30% compost+soil mix raised beds with extra kelp and rock phosphate. I understand onions need more nitrogen as well since the bulb is actually *base" of the leaves and not roots. I'm still working on growing good bulbing onions too so we can compare notes next year.
Choose shorter variety carrots for less trouble unless you have a really tall raised bed (or really deep loose soil).
Oh, also, I had WAY more problems with beets than I should have, and I believe it was due to snails eating up the seedlings, and then some kind of larva -- possibly sawfly -- munching up the leaves that did manage to grow.
Swiss Chard (which is basically beets grown for leaves) is EASY! everybody says, but mine were always full of holes -- the culprit was rose slug-like but gray-ish in color -- and never developed properly. I have one that sprouted at the base of my container grown stevia that I brought inside and is now gorwing nicely -- it's an yellow stalked one of the Bright Lights and is now about 10" tall.