Do you need anything other than approach mode to be able to have the plane fly the ILS to minimums? Do you need a EFD (glass cokpit) or can it be done with steam gages as well?
In order to "have the plane fly an ILS to minimums" - i.e. an autopilot-coupled approach - you'd need
- an ILS receiver (which would be comprised of both localizer & glideslope receivers)
- an approach coupler as part of the autopilot
- a functional display of the localizer and GS so that the pilot can monitor the autopilot's performance
- the necessary approval from the aircraft manufacturer, unless it's an Experimental aircraft
- the necessary OpSpec approval in the case of an airline operation
- all the other stuff you'd need to fly an ILS by hand (altimeter, etc)
Things you wouldn't need:
- glass cockpit (flying a coupled ILS predates glass cockpits by a couple of decades)
- digital anything (analog autopilots can do this just fine)
NOTE HOWEVER that a hand-flown ILS approach to minimums is entirely possible in most cases, and none of the stuff related to the autopilot is necessary at all. (Some minima like Cat II or Cat III with certain equipment can be the exception to that "most cases" statement.) And that also pre-dates all digital displays by decades.