I grow my carrots in the raised bed, and the nematodes don't seem to bother them. Broccoli, I grew in the raised bed the first year, but it grows a lot better in my Earth Boxes so that's where it's growing now.
My favorite sweet pepper is a little orange one I got at Home Depot called "Yummy Snacking" but there are a whole series of small orange ones with "Snacking" in the name. They're so good I eat them out of hand like tomatoes.