I don't know if you still want a reply to your original question but the Bavarian Tech website says their software will run on Windows XP which is as old an operating system as you can easily find these days. Old tends to mean cheap. Here's a link to an under $200 laptop that appears to meet that spec:
The series of operating systems was XP, Vista (usually avoided but I have an old desktop that runs fine with it), and Windows 7. This isn't everything but is what you will typically find.
Another advantage of XP (beyond price) is it runs NCSExpert. That software will do more in some ways than your BavTech software and it is "free". You can go to b m w c o d i n g.com (omit the spaces) to learn more. The key disadvantage of XP is some newer software will not run under it. Switching to a newer operating system is possible but usually costs about as much as a low end laptop.
I like lenovo laptops but dell's are OK as are Toshibas. I would probably put them in about that order. Any should work fine for occasional use like you seem to describe. Beyond operating system the other key thing to look for in the requirements is memory. But the BavTech software doesn't require much. It would seem much harder to find something that won't work than something that will.