So for Skyrim I want to be a spellsword who uses a sword and fire spell with a little bit of Archery, but I don't know if using the 3 major combat skills would work. (only ever played a full out thief in Morrowind and Oblivion)

My perks would be

Destruction
1 handed
Sneak
Lockpicking
Pickpocketing
Archery

Is this viable?

Thanks.

Almost exactly what I'm picking, except swap out lockpicking for an Armour type or alteration. The perk tree is rubbish! What race do you plan on playing?

Imperial and I completely forgot about light armor !

And the perk tree for lockpicking IS horrible, except I've love it ever since FO3

by all means use lockpicking, just don't invest perk's in it. I'll be playing a Dark Elf. And I defiantly think the all 3 combat types can work together; Destruction spell and sword for close quarters, and the bow for ranged encounters, or getting the drop on someone.