For a low cost starting point you may want to look at this ebay auction. This seller keeps putting these units on, and has 4 up at the moment (View sellers other auctions).

I believe that the motherboard is made by advantech whose specs are online, but you should check the model number with the seller. Most of the Advantech boards support disk-on-chip which would allow fast boot times, and potentially no need for a hard disk (I'm not sure how small an XML compatible browser can be made. I know that there are micro-sized X11 implementations).

It has a serial port, so should allow for the addition of a touchscreen, which the seller sometimes has available.

This is a hack job - you'd need to remove the unit from the case supplied, sort out a suitable power supply (or use an inverter) etc. But it could form the basis of a very nice solution.

Make sure you ask the seller any questions you may have! He appears to be upfront and honest about his auctions, but you probably want to confirm details - especially the motherboard model, as this will dictate whether Disk on Chip is possible or not, and power consumption. Feedback is 3.5% negatives on over 4000 auctions - not the best, but not bad either considering the volume.