Find the laptop you can afford (ie best processor, most RAM, large hard drive, weight and size for what you want to do with the laptop) and then google "install mint on XXXX" where XXX = make and model of that laptop. You will quickly see if there are any issues. If there are, pick another one!
Also, google the cost of a RAM upgrade and new hard drive for the model you pick - you may be able to save some bucks on buying a laptop with little RAM and a bad hard drive and replacing those yourself.
Finally, if buying a used laptop from a person, install mint on a usb stick and test if the laptop will boot from the usb stick and into mint.
I agree with Stephen, Latitudes and Thinkpads are usually Linux friendly
Mark