Home Invasion vs. Burglary
So first off, most of the people afraid of home invasion are rarely the ones targeted by it.
Are you involved in criminal activity where you'd have large amounts of cash lying around? Are you from an immigrant culture that would normally hide money stashes in the house? If you answered no to both of those, you are extremely unlikely to be the target of home invasion.
Home invasions are when folks are specifically looking to target you, and they're coming ready with weapons and usually several people. This is very different than house burglary - one or two people break in, preferably when no one is home, and try to get valuables and leave without a confrontation.
You can look up the stats for your neighborhood and see what the crime looks like. Also be mindful of who gets targeted - for instance, if there's a drug house on one block, that one block is going to look terrible as far as crime rates, but 4 blocks away nothing happens. You might even live in a terrible place and never be targeted for more than car break ins.
General Home Defense
Well, generally if you're not expecting to be targeted with an organized violent raid, martial art weapons become a lot more viable - it's less likely for a burglar to bring a gun, and it's also likely you're only dealing with 1 or 2 people.
At that point, the questions become - how easy is it to use the weapon given your space? Would you be able to get to it easily? Would you be able to carry it from room to room running?
A spear sounds... unlikely to be that handy. Knives, sticks, machetes, all of that seems pretty do-able. The other issue is how far away are your tools of self defense in any given space? If you have to run to one room to get the weapon, then run back to the other to deal with the threat, it's not as useful as having a few different things around the area that you can go for quickly.
That all said, if you think someone has broken into your house, yelling, "Ok honey! Stay on the phone with 911! I've got the gun!" really loudly even as a bluff will send most burglars away quickly if they've got any judgment working.
The other consideration is whether your weapons are going to be safe depending on who you live with - children, impulsive teens, folks suffering depression, friends or family who like to drink a lot or get high, people who have impaired cognitive functions... Given the rates of injuries or death from weapons in NON-combative situations, you don't want to make your home less safe in your attempt to protect it.
Vs. Actual Home Invasion
Move. Leave town. If you are living a lifestyle where you are afraid people are likely to target your home with a group of folks, looking to harm you and your family, you should move.
Most of my friends growing up were ex-Crips and folks from communities that did stash money and frankly, there's no safe, sane way to really prepare for home invasion.
Most of the people who worry about home invasion are not in danger of it, but rather hyped up on self defense machoism and privileged paranoia. Folks who are at risk either don't realize it or are living very un-civilian lifestyles that are not reasonable.