Not gonna lie, I feel like if I got mugged I'd just empty my wallet and be like "Dude whatever you need this for just ask politely next time' or some shit 'cause I am a bitch.
For what it's worth, last time I checked the numbers the first part of that is pretty much the choice that is statistically least likely to get you killed or injured. Second least likely would be running the hell away. Anything that involves escalation starts increasing the chance you don't walk away. Trying to pull a gun on a mugger is one of the faster ways to get stabbed, beaten, and/or shot, insofar as reality goes. Everything from the physics to the psychology involved pretty massively supports the offensive/initiating side of the interaction in question
Around here, "eliminate all witnesses" has become fairly common for occupied home invasions, and far from rare in other crimes, either because the criminals think that this will make them harder to catch (seems to be a safe bet, a large percentage of our unsolved homicides in the last few years are of this type) or because most such crimes are committed by druggies in withdrawal and a common side effect of such is
extreme paranoia.
If you're in good enough shape to run away, that can work, but if you're asthmatic, lame, or simply getting on in years you have no real chance of escaping the guy crawling in your window with a crowbar, and trying to whip out some kind of martial art will get you killed. So will "a single-shot small caliber gun" - such a weapon can kill, but almost never does so quickly, and it does you no good if the guy bleeds out after he's already beaten you to death.
In any self defense scenario, your only goal is "not dying", and the best weapon to do that is either an AR-type rifle (extremely controllable with very good single shot stopping power) or a shotgun (if you're strong enough to handle a shotgun with a proper defensive round - a lot of people, especially the elderly or small-framed people simply can't), but neither is particularly easy or safe to keep ready in the house due to bulk, while a handgun can very easily be kept in a nightstand drawer overnight (any sane person would lock it up the rest of the time unless carrying) with ammunition ready (it takes so little time to load an autopistol that keeping it loaded is an unnecessary risk), even a child (let alone a fully grown adult) can handle the recoil of any practical caliber, and anything larger than a .22 will do the job if you simply don't stop shooting until the attacker stops moving, then call an ambulance.
As for the police, it is a thirty to forty minute wait in my part of town from the time a call is made until they show up, tripled if the call was placed by a burglar alarm (the only practical purpose of which nowadays is to scare off people that don't know that).