Should I switch 120 AC or 24 DC with a relay?
It depends.  If you are switching mains AC, you must follow some very  strenuous rules in terms of which equipment is used, and how it is installed on the mains side. I happen to be well-versed in those rules, so I don't mind at all :) 

Not least, equipment (not components!) used in mains power must be UL listed and you must install it according to labeling and instructions, not RU component listed.  (A comparable NRTL may replace UL; CE is not one.)

In certain cases, it works out more favorably cost wise, for instance you can dive into the "parts bins" for furnace and HVAC. This can switch a lot of power (10kw) very cheaply ($35). 



However, at this scale, on the 2A at 24VDC scale, you are better off entirely switching the low voltage.  You avoid the burdensome mains-wiring rules, and you can use cheap common low voltage DC relay components found at Mouser or Digi-Key, which are RU listed as components.  (RU is an Underwriter's Laboratories listing for components.)