I will pass on my experience and what knowledge I have, with hopes both will answer your questions.
The question I have is, do you already have a desktop computer or is the Laptop the only one because that will make a difference on how you will set up ???
Inorder for your Internet connection to be Comcast, you will need to call your local Comcast office and get set up with them. You can install Comcast yourself and they will provide a modem. I stand to be corrected if I am wrong on the following but a wireless router will not benefit you without a modem. I'm not sure if Comcast provides a wireless router in place of a modem because I have Verizon at home and a router provided by Verizon. You can inquire. If by chance you have to purchase your own, then the Comcast set up should be done first, then the router installed after.
I am not the best at explaing everything, but the modem is provided by Comcast for connection to the ISP and a router which also acts as a firewall, will also allow you to connect other computers including the Laptop. A wireless connection and set up is free with the exception of the cost for the router if you need to purchase your own. Before a wireless connection can be done to the best of my knowledge you will need a modem/router. Edited to remove suggestion for illegal service.
Please do not take exception to the following but if you are inexperienced with the above, then I'm not sure how smooth everything will go even though none of it's impossible. By your questions, it sounds like you have alot of rerservations and that's why I am mentioning it. In my earlier days of learning about computers, modems and routers it was alot to understand and learn. If it was not for my experience with troubleshooting computers I may never been fortunate to have a Laptop and Desktop set up wirelessly in my house...Hopefully I answered your questions and I'm sure you will have a few more so please don't hesitate to post them back here...