There is only a single archaeological discovery of a crucified body dating back to the Roman Empire around the time of Jesus which was discovered in Jerusalem in 1968. It is not necessarily surprising that there is only one such discovery, because a crucified body was usually left to decay on the cross and therefore would not be preserved.
The position of the nail relative to the bone indicates that the feet have been nailed to the cross from their side, not from their front; various opinions have been proposed as to whether they were both nailed together to the front of the cross or one on the left side, one on the right side. The point of the nail had olive wood fragments on it indicating that he was crucified on a cross made of olive wood or on an olive tree. Since olive trees are not very tall, this would suggest that the condemned was crucified at eye level. Additionally, a piece of acacia wood was located between the bones and the head of the nail, presumably to keep the condemned from freeing his foot by sliding it over the nail.
We are not even certain about the shape of the cross. I could have been a tau (like a T) or a low Tau as is commonly depicted, but that shape came later.
Fortunately, the details are interesting, but not that important to the message.
There is a legend that it was made of dogwood. This is unlikely considering the typical size of a dogwood tree.
A Christian legend has it that the mistletoe was damned by God to a parasite’s life, because Christ’s cross was made out of its wood. Mistletoe doesn't produce enough wood, but it is my state's flower.
Numbers 19:6 KJV
"The priest is to take some cedar wood, hyssop and scarlet wool and throw them onto the burning heifer"
Although, it's not a definite answer, this may have been the Biblical indication that the cross was probably some type of cedar.
Some say that analysis of the relics of the true cross around the world are pine. Then you can discuss what type of pine. I can do that, but let's stop here.