You'll want pyrotechnics for that as magic cannot produce physical fire (physics still apply). Most people end up making staffs out of wood or just buy them (even those sold as walking sticks for hikers can be used as staffs).Tools are more of a focusing aspect than any that "give" power, anyway. The same applies to staffs.
No staffs can give you magick or powers, staffs are used as a method of moving energy, just like wands and athames.
You can never create a fireball, but you can use staffs in actual magickal practices. To make a staff is reasonably simple, you must find a long enough piece of non rotten wood and then you can keep it as is, or remove the bark carefully and carve the wood with symbols if you like.
But you have to be careful as de-barking and carving wood can result in lots of injuries, especially when knives are involved.
This isn't Skyrim, Daedric, magick can't alter the fabric of reality, we can't cast the elements, nor can we alter the DNA of anyone or ourselves. The Elder Scroll Games are fantasy, mythical, non existing,..etc.
Ok. Here is my theory: take a very strong, highly resistant wood (like ebony). Hold a flame directly onto the wood. In my experience, ebony doesn't burn (not easily at all, anyway), it just absorbs. Trees have memory in their wood, and a staff or wand is still somewhat alive, otherwise it would be rotten.
The ebony will now 'remember' the fire and has absorbed the fire without getting burnt (because it's such a strong wood). So, with incredible determination and the right timing, you *may* be able to shoot a fireball. But it is *incredibly* difficult.
Wood does not always rot because it dries before the rotting process can begin, that is all, it is not still alive once disconnected from the tree.
Ebony will burn but it is a hardwood so it can take longer. Not everyone can get hold of ebony either, it is an imported, expensive wood mainly used in high end furnature making.
Setting a staff alight is simply not safe, you have no idea how long it would take to burn down and large pieces of wood are notoriously difficiult to put out when lit, it stays as embers and has the chance to light other things on fire, especially if it is stored inside so if you plan to do this, please be careful to make sure the fire is completely out.
It may be highly magickal but all wood can burn, unless it has been treated with chemicals, some woods simply take longer than others to start; these are usually the woods that are more difficult to put out.