As a Wizard, my primary attacks (or "signature skills") all seem to involve slinging spells. If I equip a one-handed sword, does its min-max damage have any effect on my primary attacks, or do I only benefit from any stat boosts that magic weapons might provide?
Yes. Each spell a Wizard casts offensively deals damage based on a percentage unless it only has an effect. For example, Frost Nova does no damage but does freeze enemies.
Full list of skills and their damage percentages and/or effects can be found here (Note: This website is seeing a lot of traffic and is lagging a little bit): http://www.diablowiki.net/Wizard_skills
Yes, almost all of the attacks and their speeds are based on the weapons.
When hovering over a skill press the control key and it will show you how the weapon affects that spell with some actual percentage numbers.