The branches used here are cherry. They were brought down in a storm. They are a little less than 1/2 an inch in diameter. If it is too thick or too thin it could make it difficult to work with. You have to have enough space to carve a rune into the wood.
I have used yarrow stalks and tarot cards for years, and just recently have started using runes. I have found them to be very clear and helpful, perhaps they resonate with me because I have Swedish , German and English blood!
I use the Elder Futhark which consists of 24 runes. I don't use the 'blank' rune. I recommend Freya Aswynn's book Northern Mysteries and Magick: Runes, Gods and Feminine powers for people getting started with the runes. I also recommend to be very respectful when working with them as they can be very powerful, and should be used with care.
Once you have made your rune staves and are wondering what to do with them, I recommend checking out this instructable: How to Read Runes.