I have been thinking about a character and I want her/him to use these skills.

One handed swords
Heavy armor
Restoration (Fast heal and wards against dragons and mages)
Alteration(when combat starts throw up a flesh spell, mainly for paralyze at later levels)
Smithing of course

and I have a few points left over to throw into a few things like sneak and pickpocket for fun and achievements.

What would this class be considered? Does it come close to anything from Morrowind or Oblivion? Or if you guys have any new ideas that would be helpful too.

Knight/Crusader maybe?

Spellsword

Perhaps a spellsword?

Skyrim doesnt have character classes. You can him whatever for the sake of personal pleasure i guess

You sound like a pretty much straight up warrior that uses a little bit of magic.

I think it would be cool to name them soandso the knight or soandso the crusader or battlemage something like that

Paladin IMO and just because classes dont exist ingame doesnt mean they dont exist.