So, if your kids are like most, they are going to be hard on bikes. They will jump off curbs, do wheelies, and likely toss them to the ground when they dismount. I recommend something that will take a bit of abuse. A bmx will take a beating but it is an awful commuter bike. Beach cruisers are not much better - and they won't take the abuse.
I recommend a hard tail mountain bike for most kids. A hard tail is one with only suspension in the front. You will want to make a single change to it, put on some slick road tires. A slick tire mountain bike can be fast, I recently had one fly by me on a 100-mile ride (and I am pretty fast)
A hard tail is a great choice because it is cheaper, lighter, and easier to maintain than one with suspension in the back as well. You can often find them for a good price used. They will accept all of the accessories that you mention.
Whatever you do, don't buy one from a department store. A used quality bike will be much better than a brand new one from a box store any day of the week.
You will need help finding a good one, quality varies a lot. Look for brands like specialized, giant, trek, Santa Cruz, though there are many others. Stop by your local bike shop and ask if they have one used, or bring in some ads from Craig's list. If you start by saying "I would like to get a bike and have you service it", they will be apt to help you more.
Also, pinkbike.com is a good source for used bikes and parts. You can filter for bike types, location, price, etc. Expect to pay at least $250 for a used one, and that is bottom end. Process will go up from there.
I hope that helps.