Good work so far. You'll really need to treat the 'natural' wood in some way to help protect it, otherwise its going to look rather dirty in a very short time. Also, it really needs protecting from moisture and the worst excesses of high and low humidity. If you don't, a simple spilled drink could stain the wood and also cause it to swell up.

So I'd suggest a clear flat lacquer finish or some form of gun stock oil (e.g. Tru-Oil) as Andyxlh suggested.

Of course you may have already been going down this route, it's hard to tell from the photos, but you did mention only painting the front faces.