NetSurf would probably be 'the way forward' for modern browsing, but really I only go online with my 1200 to download a few files, it only has a 68030 so I don't even enable JavaScript. Currently I don't consider the 3.X branch of NetSurf to be terribly stable just yet either although if it can run on OS3.1/68030 without much trouble, feel free to point me to a .LHA of the version that can.
Try
http://homepage.ntlworld.com/cdyoung/tmp/netsurf_os3.lhaIt'll be slow though and you'll need at least 32MB. Very alpha, should be pretty stable but has other problems.