My primary birdseed is black oil sunflower. It is smaller and easier for the little birds to open than striped sunflower, and is high in oil. Fat is a very energy-dense nutrient, and essential to winter bird feeding.
You can use many styles of feeders for black oil - tube feeders, platform or hopper styles, you can even scatter it on the ground, but my favorite feeder is this Magnum feeder by Birds Choice. It holds five pounds of seed, so if I am going to be away for a long weekend, I don't worry about the feeders all running dry at the same time.
All types of little birds and woodpeckers can cling to the mesh of this feeder, and cardinals do occasionally perch on the wide seed catching tray. I used one of the original designs of this feeder, when it was two pie pans and some screening, but the newer model is superior in construction. Unfortunately, you can't take it apart, so scrubbing the inside is a little difficult.