If you want to do web browsing I could suggest getting a cheapy SFF Pentium 4 PC motherboard with a PWR Supply and nice display card. Running AROS, or for better mainstream browser compatibility an unbranded Amiga pimped full XP theme and WinUAE. A very cheap starter and it'll do what you're after X times faster than a 060 Amiga 2000.
But it won’t really be an Amiga. Will it..