Now the stain is a little more definite, but I like the darker color. It is so warm.
Actally I haven't thought of using a top coat of any other then the stain. As I sanded it with 320 then 600, it is so smooth and shiny... Should I use something? I do not want the "wet" shiny look as on some old furniture. A nice soft shine would be great...
You can get polyurethane in a number of different types of finishes. I am not sure if you can get it in flat, but I know they have it in a satin which I really like. Here is a link to a project where I finished something with satin poly:
Some of the pictures seem to have a pretty strong glare or reflection from the flash of the camera, but you have to remember that I was taking picures point blank of the project. A top coat is going to give the project a little bit of a sheen. There is a very large difference between a sheen (satin) and a mirror like reflection (gloss or semigloss).
The reason for using poly or some other type of top coat for a project like this is kind of important. Remember that your stand is going to be subjected to occasional splashes of water. If the wood gets wet and there isn't a top coat then the wood will absorb the water into itself and then you will have a blotch or water stain.
I am not sure about birch and water, but I know for a fact that red oak and water do not mix at all. Water stains on oak tend to turn black or gray from the minerals in the water. I would imagine that at the very least the birch will stain and show obvious signs of water exposure.
There are a large number of top coats out there that you could use. If it were my project, I would definately use something. There is nothing like investing the time and money into a project like this only to have it get damaged by normal use in the future.
Edit: One thing to add is that the top coat will generally add a richness to the color of the project. Whatever you use, try it on a test piece with the stain that you used. Try to keep dust levels down while applying a top coat and apply 3 to 4 coats. If you do happen to use polyurethane, you might want to get some extrafine steel wool for gently knocking down any bumps from dust particles or bubbles. Also, gently stir the poly before using it. You don't want too many bubles in the can and you want to use a natural brush to apply it. I bought some realitively cheap natural chip brushes. They work great and you throw them out after you are done.