A raised bed is a great idea - you get good drainage for one thing.
My understanding is that you always get more for your money if plants are out in the ground (or in a raised bed) than in a restricted pot, so I'd do things in pots in winter. (But I may be wrong.)
Re carrots, I was told years ago by a horticulturalist that carrots were difficult and my experience has borne that out. However, they are so popular with kids I intend to keep trying.
Also, re spinach, I've read that planting them in slight shade stops them bolting, ie running to seed before you can harvest. So if you've got a bit of semi-shade, use it for spinach; but if you've only got sun, don't worry. A sunny raised bed with compost/manure sounds like every crop's dream.