Mind the angle of the blade. Mach 3 and the like pivot and have multiblades and are basically made for people who shave wrong.
The optimal angle is very different than a Mach 3. A Mach 3 is best 'dragged' handle first, where the handle angles close you your skin, whereas a DE razor is typically best in an angle where the handle is further from the skin, closer to perpendicular to the surface.

As for straights, IMO, they're harder to learn, but if you have a good touch, they're less likely to cut than DE. Try and get the whole edges and angles thing down first, with the DE.