Buying downloading

 Do not purchase anything until you have the right equipment on hand.  If you haven't already, get a free 7 day trial to ensure it works on your system. 

https://www.adobe.com/downloads.html

Laptop or desktop makes no difference as long as it meets the system requirements to run CC + all other apps you intend to use.  Graphics and video apps require lots of resources.

And, you pay for Creative Cloud month by month, usually committing to pay for a whole year. You purchase online, by giving Adobe a credit card to charge each month. If your question isn't about Creative Cloud, please let us know.

Minimum System requirements for Cloud Programs... scroll down and check each program
-http://helpx.adobe.com/creative-cloud/system-requirements.html

Cloud Manager to install all programs https://www.adobe.com/ie/creativecloud/desktop-app.html
https://community.adobe.com/t5/get-started/how-to-activate-your-adobe-software/td-p/9636861?page=1