Programming: “Assembler” Code Language and using the right hardware

The “Assembler” Code language is hardware specific once a program is written; it can not be used cross-platform without re-writing much of it.
Question: Should I be considering any specific hardware when putting together a components list for a new computer for writing “Assembler” code. I am favoring the AMD X670 series motherboard but is it good in compatibility to start with?