Here's another link with a few photos. http://www.prewarbuick.com/gallery/1929-1934-PreWar-Buick-Gallery
I think they could be had with or without the trunk depending on the model.
I'd do some searches for vintage Buick sites although it looks like you have already done a bit of that. Some of the restorer sites have pretty good info on the different models of a year model of a particular brand.
Try a variety of searches = antique Buick, Vintage Buick, Buick club, Buick collector and what ever else you can think of.
That looks like a pretty decent old body but you are in for a bunch of wood work or wood replacement.
Here's another one. http://www.hubcapcafe.com/ocs/pages01/buic3301.htm#tell
If you can measure the wheel base that will be a start on finding the series of the car. They usually had a couple of different wheelbases for Buicks.
One more and you may get some info from this one http://www.conceptcarz.com/vehicle/z9458/Buick_Series 50/default.aspx
Thanks for the help guys. It looks like it is a 35-47. I was able to figure it out with the wheelbase and hood side grills. It turns out the 40 series had three strips on the side and the 50 and up, had four. Not sure on the year yet, but another site lists it as a 35.