If I were you I'd be tempted to get a fairly recent version of IE (say IE 5.0) - and use that.
I've used NN and IE for comparitive purpose on several occasions and I have found IE to be far more reliable.
If you're gonna surf a bit, I suggest upgrading the memory of the 486 up to its max (probably no more than 64mb) and try buying a new hard drive, (a decent 20gb hd will cost you no more than £40)
I reckon that'll do ya