Every household needs a screw driver set! You can pick up a basic set for $10 from Craftright or your classic Stanley set for $28.90. Screwdrivers always come in handy and both of these sets also come with smaller precision screwdrivers.
If you're struggling to work out what else you might need you can't go wrong with the 105 piece tool bag from Supatool. It contains entry level tools but they are perfect for around the home and for $40 you get a lot of bang for your buck! - JoshRaf
I'd suggest screwdrivers, a hammer, a drill, an adjustable wrench and a set of hex (allen) keys. - Isobel
First things that come to mind:
This really depends on what you intend to do, however the following should set you up:
You can always expand your kit and there will always be a task where you will need a specialised tool (for example, tap spanners for changing washers, saw for cutting wood/metal, etc). - darylhewston
Here’s some key tools:
Going beyond the essentials of a tool kit into tools for proper DIY you should look at the following...
Don’t buy the cheapest version of tool sets. There is a lot of rubbish out there that will need replacing too often. If you buy a quality brand DIY model it will last you a lifetime. I would suggest you visit a tool shop in your local area and talk to the tool specialist. Ask for quality DIY tools.
Most of the items already suggested from ProjectPete cover the basics. Also a set of good drill bits 1-13mm, a drill sharpener, a nail punch, a centre punch, and when buying a portable drill/driver, get Lithium-ion 18V version. If a planer is required I would suggest a hand (push) model as you are likely to make less errors. The rest buy it as you need it. - Johnnynl
A ladder. If you can't reach it, you can't fix it. - kel
I've recently just finished setting up my DIY car repair garage and if you're looking for general tools for car repair or anything related, you can check out the list of tools from Dig My Ride which I also used as a reference for stocking up on tools. - JBan26
Check out these helpful guides as well: