I build mine in an existing room, so I didn't have free rein to tear down parts of the house.
First step, Be realistic. You aren't building an Arms Room that will keep people out indefinitely, just trying to make unprepared folks look elsewhere. For comparison, a full on military Arms Room, with IDS that we keep machine guns in is only rated (by GSA) to keep people out for 45 min. You basically want to stop folks with prybars and big hammers.
I concentrated on entrance points. (mine has a window, you can skip that part) Metal (non hollow) door, Hinges screwed into 8" of laminated 2x4 studs with 6" screws, deadbolt strike plate is 1/4" steel, mortised into frame and screwed in with 6" screws. Frame is re enforced on interior corners with steel, and screwed in to framing on top and sides with 6" screws (again laminated studs) and into the slab on the bottom with 4" concrete anchors.
Pulled the drywall down, sistered up all the studs so they are 4x4, tied new studs into top and bottom of framing. Used my Hilti to double up on framing attachments to slab. Put up some .120" thick 3/4" diamond flattened expanded metal, screwed to every stud. Re-sheet rocked, mudded and painted. Honestly I left my ceiling, because of my house construction, but you could do the same thing on a ceiling, although I would use lighter metal.
It wasn't cheap, but it wasn't too horrible, and there's not a huge vault door in my house for my wife to stare out. So a good compromise. You'll need more tools than an average burglar has to get in faster then the cops that my alarm called get there.
If you build one in your basement, don't forget to run HVAC and data lines. Wi-Fi doesn't like the walls in that room.