It is certainly possible to web surf on an '030 A1200. There are several slow down points that occur on this system.
Firstly the internal serial port is the biggest one. i am not sure if you are using dial up but if you are then you need a third-party serial port such as silver-surfer. this gives a dramatic improvement, more than any processor upgrade will
AGA is also a problem, but you can improve things by:
-not using double scan screen modes- i use to use pal overscan.
-using fewer colors: maximum 64
-setting up your browser to show pictures via a picture viewer that opens its own ham-8 screenmode, for jpegs for example
-install fblit and ftext