For the most part, yes your class abilities will cost Magicka while weapon skills Stamina. However you will use both still, but if you want to focus on weapon DPS, go with Stamina. You will still have the Magicka pool available to cast class abilities, but for the most part they will focus on utility rather than damage (if you go Stamina).

I'd still recommend using class abilities and levelling up the skill lines to 50, as most of the power of a character comes from passives and there are many excellent passives in the skill trees. In addition, you cannot make a build that completely ignores one resource and expect to be viable. Your Magicka is untapped potential, which you should use to power utility based class abilities as opposed to damage focused ones. Good examples of utility abilities are Green Dragon Blood, Reflective Scales and Razor Armour.

A good build mixes stamina and Magicka abilities together, using each resource completely. Don't worry if you make a mistake now, it is possible to do a skill and attribute respec with gold later on in the game. Gold comes rather easily once you reach veteran ranks. Experiment with every skill, find out what works for you and use them. And most importantly, have fun.