The choice of internet software for a plain Amiga 500 without acceleration is limited. By far the most important one for me would be a mounter for a network filesystem. We have included two mounters, for Samba and NFS, in the package. They are covered by the documentation and example configurations.
The problem with nfs and smbfs is just that they are increasingly going out of fashion because everybody else considers the protocols too old - which is actually not an issue inside a trusted home network. There is a new Samba mounter available which supports newer protocols, but it has got other problems.
We have identified this problem.
For downloading software I can now heartily recommend the program Lubricator 2.x from Aminet and the iComp share under X-Surf/Extras . You can even launch it from there.
With this program the whole software/demo archives of Aminet and Pouet are available to you with a graphical user interface, even on an unaccelerated Amiga 500 with at least OS 2.x.
But our support has to end at some point. There are innumerous ways and solutions for many protocols such as IRC, FTP, mail, I guess even on a plain 68000, many fairly outdated, others still totally recommendable. But it's difficult to keep track and to give recommendations. This is something more for Amiga user forums.
Also it shouln't be too easy on a 68000, we still want to sell some accelerator cards.
With a 68030 browsing the WWW is just barely possible. The only problem is, there are few websites which limit themselves to such old specifications that it's any fun. But there are some fringe solutions even to that, for example by setting up all kinds of funky proxies.