Are the tools on this list enough to handle anything? Of course not! As far as I'm concerned, you can never have too many tools, and nothing makes a job easier than having the right tool.
But the point of this list is to try to choose the ten tools that every homeowner should have first - and will probably use most. You can have more tools than this, a lot more, but this list is a pretty good place to start.
Ever heard of the Pareto Principle? You might know it as The 80/20 Rule: For many events, 80% of the effect comes from 20% of the cause. I think it applies to tools: 80% of the tasks you want to do can be done with 20% of your tools. When you're just getting started, it makes sense to buy the 20% tools first.
The best general purpose, all-around hammer - the one to buy first - is a 16 oz. ripping claw hammer. You can get one of these just about anywhere, even the hardware section at the pharmacy! They come with wood, fiberglass and metal shafts. Fiberglass is a good compromise between the strength and durability of metal and the comfort of wood. Choose a decent quality hammer that feels natural in your hand.
Tape measures are so handy that my wife keeps a small one in her purse. For most home projects, a 25' - 30' works well. I prefer blades that are 1" wide because the extra width provides a lot of additional support as you extend the blade. Choose one that is easy for you to lock and unlock and that has numbers and markings that are easy for you to read.
An inexpensive cordless drill with a keyless chuck will probably end up being your most-used tool. Find one that fits your hand well and feels well balanced. Make sure to include a set of drill and screw bits for the most versatility. I wouldn't recommend anything less than 12 volts. If you want to delay making this investment, get a 6-in-1 screwdriver and forget about drilling holes for now.
There are lots of different types of pliers. Most people probably choose slip-joint pliers for their first pair. When you think "pliers," this is probably what you see in your mind's eye. But I think your first pair of pliers should be the most versatile, and to me that means groove-joint pliers. Their angled jaws make it easier to get in tight spaces and the jaws can grip much larger objects than their slip-joint cousins. Select either the 8" or 10" size with cushioned handles.
An adjustable wrench is the ultimate multi-tasker. Infinite adjustability means that you can use this wrench to tighten or loosen almost any size of nut or bolt that you are likely to encounter. And you don't have to worry about metric or SAE. One size fits (almost) all! The 8" or 10" size is suitable for most homeowner applications. A padded handle can add a lot of comfort when you're trying to loosen a really tight nut.