I don't have conures, but 2 of my parrots are approximately Jenday size. You're going to want to get a cage which is a minimum of 24x22" or about. The next standard size up would be ideal. While they're fairly small parrots, they will enjoy space to move around and play when they have to be in their cage, and of course bigger is always better for any bird species. Keep in mind about bar spacing though. A bar spacing at about 5/8" is ideal. 1" is too big for a Jenday size bird.
You will need to teach the bird at least the basics of positive reinforcement. Clicker or target training are good methods. Any conure can be worked with and taught to be socialized with multiple people if taught consistently from an early age. Remember, you get out of it what you put in. Conures are highly trainable. If you hear that parrots are one person birds, mean, or unruly in any way, you can bet the bird lacks basic training and boundaries being set, and bad habits are not nipped in the bud by the owner.
Diet for conures are the same for most Psittacine species (parrots and parakeets)... High quality pellets, fresh foods with or without added grains, sprouts, seeds, (or at least some of those things if not all). A high quality pellet base to the diet assures adequate nutrition is covered.
Parrots (even small ones) are headstrong and smart, and will be a learning curve above budgies, but the conures are considered to be a great choice for novice level owners
. Keep in mind the Jendays and Suns are known to have a very loud voice compared to their body size, and can be a vocal species. All the best to you