Initially, I planned on using 1x2 for the battens, most likely cutting down 2x4's on my table saw. While I was in Home Depot, I saw bundles of fir lath - 60 pieces for $10.
They are 1 1/2" wide and about 3/8" thick, which gives enough of a shadow-line to look good. I mounted them with a thick bead of tite-bond wood glue and a few staples. About 20% of them had splits or bad edges, but I can cut these down for use above the doors and windows.
Once all the battens are up, I will spend a good amount of time caulking the them, plus the lap siding gaps and trim.
A tip on installing lap siding: insert small pieces of #15 roofing felt at the ends of the siding to make sure water does not penetrate at the joints. Any water that does go through the caulked joint will be directed right back out again.
In this case, my DW cut a bunch of 4" x 6" pieces, and I slid them in before nailing the ends.