How can I build a lamp like the one I saw in the store?
It is great to begin woodworking with a custom made project that fits your needs. Often doing it yourself can result in a significant savings, but I think you may find that purchasing the components for the lamp may well cost more than the amount they are asking. But your version will be the size and finish you want.

For the linen panels, you could try mounting the linen on thin plastic, such as acrylic, cut to size. You could use spray adhesive, such as this one, or you could tension the cloth and glue the edges with a thin bead of a general adhesive.  Just make sure it will stick to the type of plastic you select and do a small test to make sure it does not discolor the fabric.

Screw length should be enough to go through the first piece and 1/2 to 2/3 of the way through the second. You need to pre-drill all holes. Glue will stabilize the piece.

Finally, be sure to leave the top of the lamp open to allow heat to escape, and be careful when stapling over wire not to nick the insulation.  You should consider attaching the wire with a bead of glue along the length instead.  You can hold it in place with tape until it dries.