Not every Intel... you should be safe if you use a Core2Duo, but only if you Libreboot it, which means you will need to do hardware changes unless you buy one that is directly modified by someone you can trust. There are some Laptops like the Thinkpad x60 which only require you to flash the bios and do some changes without modifying the hardware.

If you want it to be ME free by default, you have to go as back as Pentium 4...

With AMD, you have PSP, so it's the same, and you can't disable it, we know less about the PSP than the ME. You would need to back in time too, I think 2013 was the last year it was PSP free. Still faster than a Raspberry.