I think you can match up practically any computer to an appropriate emulator.
I've run MAME 36 set (somewhat tweaked) on a Pentium 3. Running "Metal Slug" and all

I have a 486 kicking around that I was thinking of trying Vantage on.
These are desktops but I think you get it.
Just buy any laptop you can afford. I happen to like Gateway models that have quick access to the CPU from the bottom. Once you have the laptop, try a few different versions of MAME on it, like MAME 36, 56, 86, etc. See what version runs well.
Also see "Black Vipers" guide to disabling services if running Windows. You can free up a lot of resources. Windows is pretty bloated out of the box.
Various versions of MAME have been running on computers for over 15 years, so whatever you get can probably be made to run an appropriate version of MAME well

Cheers,
Craig