first of all, if you're underage, a parent will have to sign any contract, if one is involved...
next... rights:
'first serial rights' means that they only have the right to publish your story once... after that, you can no longer sell that piece to a magazine that wants those rights, but you can sell it to those that take 'reprints'... but you have to honor the time period mentioned in the guidelines of the mag you sold it to first...
'anthology rights' means that if that magazine ever prints a collection of the stories they have published, they can include yours and don't have to pay you for it again, unless that is specifically mentioned...
your characters and settings are your own, to do with as you wish... you can use them in other stories and it won't affect rights given with any of the previous stories you've sold...
go to
http://www.anotherealm.com/prededitors/ for explanations of all the stuff that's confusing you... and to make sure the publishers and such you're dealing with are legit...
love and hugs, maia