Your needs will also vary depending on whether you are just going to build a house and buy things for it or whether you are going to have a go at making things for it. My list assumes the latter.
I presume most households have things like scissors, a small hammer, tape measures and those sorts of things.
These are in no particular order of usefulness.
Clamps of any sort. These are a couple of sets from a dollar shop. If you see any cheap small clamps buy them they always come in handy. The other 'clamp' is elastic bands - really useful for holding box shapes together while the glue dries for example.
Storage: you can not have enough good storage. Vital for being able to find what you want. Again cheaply bought when I see them at a good price. My mainstays are under bed boxes - mine have wheels which makes them even better for sliding in an out under the work surface. The plastic boxes in the background were bought for two dollars each from the bead section of Walmart. They are divided into smallish sections and are perfect for storing all the teeny things to dress a house or findings etc for making things. I am going to cheat here and add in something which takes me over my ten. You can just see a green cutting mat in the photo - essential to keep your knives sharp and surfaces cut free.
Toothpicks/cocktail sticks are the most important tool on my desk. They have endless uses - the most obvious is for applying small amounts of glue but they clean up paint and a seem to do a myriad of other tasks. This is my stash in a drawer.
Sanding. I didn't say sandpaper because I don't use it much. You will need about 400 grade for most things you do. In the main I use those blocks that you get for manicures. Again very cheap and as they have four sides they last ages and are perfect for fine finishing a piece of furniture.
Brushes. Gather as many cheap (but good) brushes as you can as you bowl along. You can find some very nice sets in hobby shops and it is worth having any old shape and size they will always come in handy. Among them you will discover the one you like best for this and that. I like small straight edge brushes for most painting. Don't be precious about them, be prepared to pass them over to the glue brush store when they aren't up to scratch - use them for glue so you get a bit more life out of them.
Mitre block and saw: This is an essential piece of kit for cutting skirtings and other mouldings. You can buy a large pair of scissor-like right angle cutters which people swear by but I have never tried them. Making good corners is all about practice, practice, practice.
Right hand jig. This has been a real bonus tool for building kit after kit. I have the small (again, cost cutting) magnetic version but it has served me well. You can glue wood together using the right hand corner to keep things squared up and lock it in place with the magnets and leave to dry. You can easily make a right hand jig yourself from scrap wood or Lego and I had one of those before this one but, if you can find one of these and can afford it I commend it to you.
Steel Rule. Absolutely essential for a straight edge when cutting materials with a knife. Mine does not have a finger guard and I have a shaved thumb to testify to that. If you have to buy one, invest a little more and buy a straightedge with a guard.
Knives. Like me you will read time and time again that the safest knife is a very sharp one. This is absolutely true. You will need a good Xacto knife and a lot of blades.
I hope this is a help. Anyone who has another essential piece of kit please let us all know in the comment section below.