So you've got yourself a broadband connection (cable modem or DSL line) and now you're ready for the Internet? I've got news for you, the Internet is ready for you - more ready for you, than you are for it.
All machines on the Internet are vulnerable to attacks, regardless of their operating system. Windows systems just seem to be more vulnerable. Most people do not apply updates to fix Microsoft bugs. Since Windows is so common, it's also the operating system of choice to be attacked.
Your machine will be attacked, whether it is using a dial-up connection or a broadband connection. 100% guaranteed. This is not a bet, but rather a certainty. The only difference is that dial-ups get attacked slower because they are connected less often and the connection is slower. You are no safer just because you have a dial-up connection.
Your Cable or DSL modem provides an Ethernet connection to your computer. It looks to your computer just like it is at the office on your local LAN. This makes it very easy for you to connect - you just plug in a cable. It also makes for a very fast and easy way for other machines on the net to attack your machine.
A router is a box that sits between your machine and the cable/DSL modem and the outside world. It intercepts all the cruft coming in and throws most of it away. If your machine starts something like a web connection to some site, the router lets that data go out and come back. Anything your machine did not invite in, it tosses out. This prevents most kinds of attacks from even getting started.
You absolutely must have a router for your broadband connection. Don't use your new connection for one second one without a router between you and the bad guys.
I've been using a Linksys router, like this for several years. There are several other equally good routers on the market. I have no relationship with Linksys, other than being a happy consumer of their products for many years. These are now very cheap ($60 and less). They are effective. They are easy to set up. Run, don't walk, to a nearby computer store or order on the Internet and get a router and install it right away.
I can't emphasize how important this is. It does you no good to reinstall Windows if your network is completely vulnerable. You won't finish the install and updates before your machine will be re-infected, perhaps to a state you'll never recover. You can be right back to where you started before you ever get going.
This is not an option, if you are serious about keeping your machine usable.
Laptop computers pose a special risk because they come in and out of your home network. You may secure your laptop at home behind a nice, safe router. Sometime later you will pick it up and go out into the big bad network world where you aren't protected, get infected and then bring your infected machine back into your home where your laptop attacks your other machines.
So you can't always trust that your machines at home are safe. Even if you are protected by a router, each and everyone of your machines needs to have all the protections I describe because you never know when something will get through. Laptops are just one obvious way to infect your otherwise safe home machines.