2nd vote for Ibrowse over Aweb..it's a much better browser.
Genesis works well but i prefer MiamiDX.
If he was looking for the better browser he would probably not be sitting on a classic Amiga. Personally I think AWeb has the advantage of being free, fully working and, well, available at all. It also runs quickly on modest hardware (even in Amiga terms).
As for a network stack I would suggest AmiTCP (again free and unbloated). I remember that there was quite a thorough guide on how to install it properly, which got me online.