Why do I need to worry about getting a "good" mouse?
Odds are you're spending a good chunk of your day in front of your computer, and having a machine that does what you tell it to is a big part of the experience. Having a really good mouse, like getting a good chair, is going to make the good bits more pleasant and the bad parts less aggravating.
Of course it goes without saying that you can use anything, even an older laptop touchpad, for a while. But it slows you down, it's not pleasant and it's really just frustrating to deal with. Like a reliable internet connection you just want it to work.
Let's talk about some general tips and then go into the specifics.
The old rolling ball style mice are pretty much impossible to find these days as are the PS2 connectors. Your choices are going to be between USB and Bluetooth connectors and the different kinds of sensors.
By the way, the gaming / work divide applies here as well. A gaming computer is great for doing work on, but a work computer will suck for gaming, in the same way a gaming mouse will almost always be better than "business" mouse.
USB / Bluetooth
In general, most of the Bluetooth mice I've seen have had issues with accuracy and responsiveness as well as just randomly disconnecting. Interestingly price is not necessarily a factor in this, as I've seen really expensive mice repeatedly fail to connect. I'll go into more specific examples later, but if you're looking for a wireless mouse you're better off getting a mouse that comes with its own USB receiver than one that connects to the computer directly over Bluetooth.
Beyond that USB is always more accurate and more responsive than a wireless mouse, even the very good ones. I don't think it's a question of bandwidth as much as the fact that the cabled mice don't need to conserve battery and don't go into power saving mode, as well as being able to be more aggressive with the sensors that they have.
The single biggest problem with wired mice is the cable management. Though modern mice have fairly thin and flexible cables, you need enough space behind the computer to make sure that your cable doesn't pull on anything. On a laptop I usually prefer to plug the cable into the USB port on the opposite side of the machine and let the cable coil on the desk behind the laptop. This works very well but you need a desk with space behind the machine. If your desktop tower is on the floor under your desk, odds are good your cable will pull against the desk and you'll notice it every time you move the mouse. In that case I'd suggest getting a USB extension cable, pinning it under a book or something and plugging the mouse into that.
In general your choices are between a red/blue illumination and an invisible laser. The illumination will highlight the surface under the mouse and the mouse sensor will then scan the result and calculate motion based on that. I've heard it said that the invisible lasers have better accuracy on glassy and reflective surfaces but suffer from acceleration problems. For my part I've been impressed by their accuracy and have never noticed strange acceleration, so I'd recommend laser mice beyond normal red/blue sensors.
So at this point your ideal mouse is going to be a cabled laser mouse. Which you can get for around $10 AUD at the lower end. Now we'll go into more specific details.
I've used these fairly extensively and I'm a huge fan of them. There are better choices, but as a very cheap wireless laser mouse that provides excellent performance they're a solid choice. One very major issue they have is that their wireless sensor is only really good for about 10cm, so they basically only work for a laptop where the sensor is on the same side as the mouse itself. In that situation, they're perfect. In other situations you're going to have a lot of skipping from these.
This is my current personal favorite. It's a cabled laser mouse with a clickable sensitivity button that I almost never user. Personally I toggle sensitivity in Windows to about half of the normal value and just leave it there for ideal precision. Precision wise it's perfect, and the weight has a good feel to it. That being said it's also slightly heavier than I'm used to so switching between typing and the mouse quickly felt a bit strained at the start, but it's something that I got used to fairly quickly. The accuracy is perfect, no issues at all, even better than the M165 though that could just be my impression as they're both almost perfect.
Magic Mouse 2
The magic mouse is a Bluetooth connected laser mouse. Given Apple's normal build quality I had high expectations, but ultimately this works better as an art piece than an actual mouse. Aside from the random Bluetooth disconnections that don't happen with other mice on the same machine the mouse feels strange to hold, the clicks can turn into drags randomly and worst of all, the accuracy doesn't seem quite as good as a cheaper gaming mouse. When you're using it it's just ok, but you'll find yourself reaching for the Macbook Pro's touchpad if you're on a laptop, which is much better... at which point why even bother with a mouse? It only really helps if you're using a desktop, but at that point there are larger wired options that would work much better for you than a portable wireless mouse.
Microsoft Modern Mobile Mouse Bluetooth Glacier
This one's surprisingly good for a Bluetooth mouse, at least in my experience. The accuracy is good and it's very responsive. It also looks good sitting on the desk and the magnetic battery panel lid is a nice touch. It's a Bluetooth mouse that uses a blue LED to illuminate the surface. In my experience it's better than the Magic Mouse 2 despite being less than half the price at $55 AUD when not on sale. I have seen it skip occasionally though. It's rare and I haven't ruled out that it's a software with the computer issue, but knowing that it's a wireless mouse I'm not entirely surprised.
In summary if you have the choice of any desktop mouse, I'd suggest getting the Logitech G203 with the caveat that you might need a USB extension cable pinned up to make sure that the mouse cable doesn't drag on anything. If you're traveling you might do better with the Logitech M165 a very lightweight wireless mouse that's almost as good.