If you plan to use Mach3 then really you need a Desktop machine or dedicated motion control card to use with a laptop.
Reason being that most laptops have energy saving features and will shut down the parallel port or other little used process to save energy and this causes big problems to the control software.
The only safe way to use Laptop is with an external motion control card but these are expensive and can cost more than a desktop. They do work much better than PC parallel port and give much nicer running machine but it costs you.

Don't know if Linux CNC is ok with laptop or not.? Linux CNC is free and you need to be pretty Ok with PC's and setting up operating systems etc but other than that it works good I'm told. . . . . That said Thou if your new to CNC and not PC savy then I think you'll find Mach3 much more intuitive with lots of help and advise readily available.