A common size is 3/4" x 1/4". A better size for most applications is 3/4" x 3/16".

3/4" x 1/4" is 19mm x 6mm in metric measurement. I have built most of my sea kayaks with 19mm x 5mm. I have built racing kayaks from 19mm x 4mm and from 20mm x 3.5mm. My most recent sea kayak was built from 22mm x 5mm.

Unless you have a good reason to use a different size, 3/4" x 3/16" is a good starting point.
This site has a good explanation of the advantages and some hints about bevelling.
http://www.laughingloon.com/shop.tips.html

Don't assume that you have to run them through a router. I have built 12 strip built kayaks and have not run a single strip through a router. Some of the well respected professional builders also use bevelled strips rather than bead and cove.