What are the best basic yoga positions?

Depends on what you want to accomplish. It's hard to answer this question fully without knowing what you want to achieve with yoga. Are you looking to become more flexible? Gain more strength? Relax? Do you have a specific issue you want to address? "Best" is also relative. "Downward facing dog" is one of the most common yoga poses. Does that make it one of the "best"? Personally, I could do without it. It doesn't calm me down, it stresses out my elbows, and I'm not getting more flexible by doing it. There are also better ways to strengthen the arms, in my opinion. (I'm not a yoga teacher, though.) My favorite "basic" yoga poses are standing or sitting forward bend, any sort of gentle spinal twist, and the basic standing warrior poses. I am sure there are others I have forgotten. You might want to take a few beginner's yoga classes to experiment and see what you like best.

Refining the question.... ...will help devlop the answer here. There are some foundational poses (asanas) that are appropriate for raw beginners. These poses allow the student access to the pose, provide some simple experience of them, and allow the student to begin the process of increasing self awareness which includes spatial perception. In addition, such poses provide a framework onto which other poses may be added (only when the student's mind and body are properly prepared). My sense is that you are asking for a list of this or that so I'll provide such a thing with the caveat that there really are no "best" poses nor are there really any basic poses unless those terms are placed in a context. Virasana - Hero's pose Tadasana - Mountain pose Adho Mukha Svanasana - Downward Facing Dog pose Uttanasana - Standing forward bend Baddha Konasana - Bound Angle or "cobbler's" pose Supta Padangusthasana - Supine Hand to Big Toe pose Trikonasana - Three Angle or Triangle pose Parsvakonasna - Side Angle pose Virabhadrasana I - Warrior 1 Virabhadrasana II - Warrior 2 Bhujangasana - Cobra pose Setu Bandha - Bridge pose Sirsasana - Headstand Sarvangasana - Shoulderstand Savasana - Corpse pose I have ommitted twists, and included the two inversions but I've done so with reservations for twists should be included and beginners should NOT do headstand and shoulderstand without proper instruction (from a yoga teacher).