Any commercially sold computer within the last ~10 years will be able to run DF.
DF isn’t GPU intensive but it is very CPU intensive. However, since the game was started before multi-threading became a thing, to run very large forts at a decent FPS, your CPU has to have very good CPU for single core.
If you do happen to take a look, make sure to use the starter pack (google DF starter pack) by Perry.
DF is the only game so far where I would say, “Try it at least once, for a few months” before you die.
With the new update coming out (taverns, visiting adventurers, music and poetry), its up to you if you want to wait a year for this next major update or to enjoy the current version now.