A lot has to do with how a familiar a person is with the gun. A well trained person, like an infantry soldier, can pick up an AR at any state of: loading/safety condition/ Mag in or out and get shooting fast, being under great stress or not.. A very well trained individual can use muscle memory to get the AR shooting, their actions being automatic due to intensive training. For these type of people any condition can work.
For folks of lessor training, the more actions it takes to get the gun shooting in panicked conditions, the more failure is likely. Loaded safety on is probably the best bet.
The other big consideration, relevant to training, is how stressed is the user (panic, fright, surprised) due to the home invasion. A person should train thru mock invasions, to get to where the gun is. You don't want to stay surprised, panicked and frozen in the recliner, when you should automatically be up and headed to where the the gun is. Personally keep a 38 on the end table next to the recliner.
Personally I use a 12 gauge pump, action closed on an empty chamber, trigger pulled, safety off, magazine full...so all I have to do is work the pump to get it going. I hunt or shot clays at least 60 days a year, so my muscle memory on a pump action is good.
Carried an M16 or M16A2 for about seven years in the infantry, and still fire an AR a lot. I would go bolt closed on an empty chamber, safety off, trigger pulled, magazine loaded. In this condition, pulling the charging handle gets the gun running, I want this second to make sure things are as they appear.