Hi Sue
I'm guessing that it was you who asked the same question on another genealogy forum and you therefore have long answers from me and others there as well as the ones above on this forum. However, without in any way meaning to be rude I'm guessing that you are not very computer literate (as the phrase is) because you ask about moving your internet onto a new machine. Forgive me if I oversimplify by way of an answer.
The internet is not really yours or mine. It is just out there in the ether. Neither is it on or in your machine, so when you turn your computer off at night the internet is still out there working away. When you access the internet you do so by opening a window into it using a piece of software on your computer called a web browser. A famous one is Internet Explorer which may be what you use.
There are lots of different free browsers you can download if you don't like the one you are using, or the one loaded on your new machine. They all do the same trick more or less and new computers usually come loaded with one. PCs, including laptops which use Windows operating systems, often come loaded with Internet Explorer or Microsoft at least advises you to use it. But you could download Firefox, Chrome, Safari or various others and they all enable you to connect to the internet.
You can also use more than one browser on your machine if you really want to. Some work better than others at various tasks. I recently bought a Mac laptop which has Safari but it is not very good at reading the DJvu images available to genealogists of census pages. So I simply downloaded Firefox for that purpose and it works fine.
So don't worry, the internet will still be visible when buy your new laptop, even if you go wireless! Someone else has told you how to transfer your Favorites (in IE) or Bookmarks I believe but if you get stuck doing that ask again.
Good luck.
