First, windows 7 - 64 bit should also run 32 bit apps but it will NOT run 16bit apps (except in Virtual XP mode). Win 7 - 32 bit will run 32 or 16 bit apps but not 64bit.
Your biggest concern with upgrading will be in finding drivers for older hardware - printers, trackballs, etc and the drivers may exist in 32bit but not 64.
Two things that can help (but these are not perfect) are the compatibility center ...
http://www.microsoft.com/windows/com...s/default.aspx
I searched Timberline and Expedition and found no matches.
And the Upgrade Advisor ...
http://www.microsoft.com/windows/win...e-advisor.aspx
You might try installing this on a laptop they currently use - this may tell you some hardware issues like not enough mem but you don't care about that if you are getting new equipment but you might look for software issues.
Unfortunately the more obscure/ancient the equipment/software the less likely someone has added it into these tools. The compatibility center has a feedback section where the user can recommend an addition but not being there is not the same as a green light.
Also worth mentioning since you are ordering new equipment. Many companies ship with less than the recommended memory. For Win 7 64bit 3GB is recommended (and technically it is closer to 3.25), Win7 32bit 2GB is recommended.
I personally normally recommend 64bit but if 32bit is more compatible with their existing software, well win 7 32bit is still better than XP 32bit. However if it absolutely will not run on Win 7 even on a 32bit machine I doubt they will be happy using Virtual XP under Win 7 for everyday applications. Best recommendation is get one laptop and test it.
I don't think Dell is any better or worse than HP. I would say for construction people don't get those paperthin macs that bend if you push your fingernail into em too hard (ok this may be an exageration).