Wireless describes one of two methods of communicating information with a network or the internet, wired is the other. DSL is one type of ISP provided services, others are Cable, Satelite, dialup, and mobile broadband like you use currently. First you need to decide what type of connection you wish to use, Dialup is typically the slowest but can be used from just about any phone, companies can setup connections which are high end dialup connections. Though T1 is faster than normal dialup, it is also quite expensive for consideration for personal use. Most common for home users are DSL and Cable depending on availability in your area. With DSL you pay for a specific connection speed usually available in different packages from your provider, usually those listed at like $19.95 per month are 756kbps download and 64kbps-128kbps uploads, and the ISP will offer faster speeds for more money per month. Regardless of which speed you select with DSL, you always connect at that specific speed setting. With Cable, again depending on your area, your connection speed will vary up and down depending on how many others in your immediate area are using the connections as well, the total bandwidth for connection is shared across all the users in a given area as set by the ISP. So when user levels are low, you will have much higher download speeds up to around 16mbps typically. When there are alot of users in your area online your connection speeds can drop quite low.
DSL is a fixed connection speed all the time because its dedicated to your house where cable is variable based on the number of users active at that time. I use Cable, Cable remains live 24/7 unless there is some form of service interruption, I do not have to establish a connection each time I sit down at the computer, I just turn on the machine and click the Internet Explorer icon and I am online. DSL can be set to auto log in but it is a manual configuration, the default will require you to enter your password everytime you start or restart your computer. Most top end DSL packages cap out at around 1.5mbps-2mbps download speeds.
Now that you have selected your connection provider type, you need to decide if you are going to use a wired or wireless connection. Obviously stated, a wired connection limits the distance your computer can be away from the router or modem by cable length. It is possible to get the house wired with built into the walls connection ports so you can more easily move your computer from room to room, but wireless is alot easier in this regard. To use wireless with your connection type, you will need to install a wireless router or access point after your modem from your ISP. Wireless connection points come in various single and multiple connection speeds using letter ratings. Ratings for wireless are listed as 'A', 'B', 'G', and 'N'. 'A' type connections are rarely used anymore, typically found are 'B' / 'G', 'G', or 'N' connections. 'A' standard is a 2mbps connection, 'B' is a standard of 11mbps, 'G' is a standard of 54mbps, and 'N' is a standard of 108mbps. Actual data throughputs can be different with any of these connections, some 'N' routers actually state data throughputs can be as high as 350mbps. The current standards accepted by most wireless users today is 'G', the 'N' is currently under review and revision as the next to be accepted by the FCC, but at the moment it is listed as draft because it hasn't been formally accepted by the FCC.
Most laptops that have built in wireless adaptors, are typically 'B' / 'G' connections. So you select a wireless router or access point, my recommendation would be the Linksys WRT54G router as described in this link: http://www.linksys.com/servlet/Satellite?c=L_Product_C2&childpagename=US%2FLayout&cid=1149562300349&pagename=Linksys%2FCommon%2FVisitorWrapper&lid=0034908483B02 . It is fairly common and easily acquired from many stores for a price around 39.95.
I hope this helps you with your query.