with a bit of care you should be able to surf on that: choose your screen mode carefully (I suggest Super72 if you can bear it, or productivity), better to use 64 colours, and have lots of RAM !
I used to surf with a similar setup on dialup until I got my A1XE - its still dialup, but much more fun !
my old setup:
A1200 with Apollo 1230 lite (25 MHz 030 + FPU) and 8MB of Fast RAM, and a 2.5" HDD. you might be better advised getting a SCSI board for the Blizzard, that should speed things up.
OS3.9 was intended to run on an 020 with 6MB RAM minimum, but was good on my machine - should be good on yours too !
If you want GFX, you can get a PCI busboard* that goes between your blizzard and the Amiga - but you will need a tower to put it in !
go for it, and let us know how you get on !!
(* not sure if these are still made, but Elbox is a good bet)