Debian can be pretty light/small on a clean install and xfce should run fine on 2gb. Although the biggest thing is gonna be if the laptop has fast storage or not. Since its a celeron it might not be upgradeable, and if it doesnt already have an SSD any desktop will feel slow
Personally if I really wanted to squeeze all the performance I could for web browsing I'd go with minimal Debian and RiverWM but thats a bit more involved
My solution has entirely just been to own less things and designated spots for every item. The main problem is forcing myself not to get cool things I will never actually use