I don't think I've ever been to Burnham Market, and I've only ever passed through Hunstanton about once and can't really remember much, so I can't really comment on them.
Spring is certainly a better time on the Norfolk coast in many ways, not just because of the better weather but also because places start to open up more. The beach districts of many seaside resorts can often feel like small ghost towns in the middle of winter.
Yes, Great Yarmouth has a very long, wide beach. It's the major resort on the east coast, with an extensive parade along the seafront with dozens of amusement arcades, hotels, restaurants, fun-of-the-fair kiddy rides, burger stands, etc. Brittania Pier also has a theatre, along with a bar/pub, children's rides, the usual fairground-style stalls, and so on. Think Coney Island. The north end of town is quieter though, still with wide, expansive beaches, but the surroundings are more garden walks, quieter hotels, and expensive seaside houses.
Gt. Yarmouth is really the place to go if you want to the hectic fun-of-the-fair seaside atmosphere. Cromer and Sheringham are much more restrained, almost "gentile" places by comparison.
If you're staying around Sheringham area though, Great Yarmouth is well within reach of a day trip.