To be honest, i have my a1200T and to use it for web browsing is well... a little dissapointing compared to PC's nowadays. You need to get a decent Graphics card installed to get off the "AGA" look that you have stock, but even then dont expect miracles to happen (remember it IS 10 years old!)
Saying that, lots of people use a1200's to browse the net as their only connection, maybe they can list the pro's rather than the cons.
But remember, AGA is slow, and your limited to the types of websites you can go onto.
Cheers
Kev
-edit
Check my sig for my a1200 spec - you will see it aint that great lol!
:-D