IBrowse2.3 is damn good and is very efficient. I bet it would still be good on '020 + 8MB. It can do SSL & Javascript, page layout is fantastic, image dithering is excellent, it's fast and resource friendly.
I would reccomend for web browsing something around '040 40Mhz. The '030 would be too slow for prolonged surfing but if you did so then IBrowse would be the browser for you. As for classic gaming then the '030 would be your BEST option as it is fairly sociable to older code.
Wordworth, Deluxe Paint, TurboCalc, Pagestream - all killer apps for Amiga.
Towering your Amiga has long been an issue of contention for many Amiga owners as the original case is so compact and you can simply plug things into the PCMCIA port (ethernet, CD-ROMs, SRAM, serial port, samplers etc.) - if you do tower then a Zorro busboard will allow you to put a nice GFX card in. A Piccaso-2 would be dirt cheap and would speed things up bigtime.