I just wanted someone who used swords and magic
In that case, alternate classes (and sub-classes) you may prefer over paladin:
Bard - not a usually a front-line fighter, but supports the party with spells as well as using weapons.
Fighter: Eldritch Knight - you don't take the sub-class until 3rd level, but fighters are pretty powerful and Eldritch Knight uses magic similar to that of a wizard
Rogue: Arcane Trickster - again, you don't sub-class until 3rd level, and you're going to be using wizard spells. A rogue gets their sneak attack bonus on finesse weapons, such as rapiers, as well as on ranged weapons, so you can really deal some damage both physically and magically.
These are just the options in the core book, there are many other supplemental books with even more subclasses of the existing classes. Your DM may prefer that you stick to the core book, which is understandable. Another option is multi-classing, where you level up as, say, a fighter for a few levels, and then start taking levels in, perhaps, sorcerer.
I just ran out to the living room to get my PHB and look stuff up for a forum post, consider me obsessed with D&D.
My roommate and I both get over-excited and recommend classes till people's ears fall off. Feel free to either disregard me completely or ask me more questions, I'm ears-deep in two different 5e campaigns at the moment, so I can make recommendations of what I've seen of various classes in action.