As is mentioned above, just think of a laptop as a regular computer. They're really no different. They'll do everything you want.
The main advantages they bring to most people over desktops is that they less cables. You may now have a mouse and keyboard connected, with a monitor cable, and power cables for your computer itself and the monitor. You could just have a power cable for the laptop.
If you wanted to use a mouse instead of the trackpad, then you just need to buy any USB mouse and plug it in. Most are USB now, if not all.
If you currently connect to the internet by plugging it into a modem (I assume you have broadband), then you just do the same. Laptops have the same ports on them that most PCs do.
Most laptops now are also wireless enabled. This means that if you have a wireless router (about �40 or so), you can sit with your laptop wherever you like in your house and use the internet.