'appbrowser' uses a script called 'tce-load', which itself uses Busybox 'wget'. It then depends on the mirror your are using, so for HTTP it's port 80 and for FTP it's 21. No port 443 AFAIK.
My simple test for HTTP connectivity is to try
wget http://example.comThe most primitive "browser" would be 'wget', but that's a bit of a struggle to "read" a web page (e.g. via 'less'). I think the conclusion in this forum is that Opera 9.64 (i.e. the 'opera.tcz' extension) is the "smallest" of the "complete" options.
There are smaller ones (e.g. 'chimera2.tcz' or 'dillo.tcz') or text-only candidates, (e.g. 'links-cli.tcz') but with most of them you will struggle to login to this forum here. There was a
thread not that long ago, where this question was raised. IIRC I could not work it out myself (i.e. how to use 'links' for that purpose).