Do you know which is the latest web browser compatible with Windows 95 / 98? At the moment I have an Opera 10 working fine; it is very lightweight but very outdated.
I assume that software that works in Windows 95 will work in Windows 98.
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That latest web browser I am able to find is K-Meleon 74 Windows 9x Edition. It was created in 2014, when the Pale Moon engine (Goanna) was backported for Windows 2000. It requires KernelEx (and the latest updates) and a rather beefy old machine to run.
You could also experiment with other later browser versions on top of KernelEx, as it adds NT support to Windows 98. If not, then you're stuck with the official latest versions, of which Opera 10 is probably the best.
I have not tried any of these, not having a Windows 98 system, but a bit of research reveals:
Browsers carried on supporting Windows XP for much longer, because it was a better platform for software development and testing.
This answer was written before the question was edited to add Windows 95. It's not safe to assume that anything which runs on '98 will run on '95; the reverse is more likely to be true.
It very much depends on what you're trying to do - Lynx's latest release is from 2018, runs on Win95, and is very lightweight, but, you know, lacks graphics.
I also use Dillo on old machines when I just need Wikipedia. (Yeah, it does not have nice prebuilt Win binaries as far as I can tell.)
// would've like to comment, but I lack the reputation!
IE6 was the last Internet Explorer on Windows98 SE and IE5.5 with high encryption pack for Windows95. These were important for Citrix, and quite a bit of software leveraged IE6 dll's, notably Ultra-Edit.
Seamonkey 1.1.19 - March 2010, a bit Retro. Not as recent as a better answer.
I think this is an XY problem.
If your goal is to surf the web using a really old computer, the best bet is to install Linux on it and use a modern web browser.
Web standards have changed DRAMATICALLY the last 10 years. Almost no website will be usable due to the proliferation of jQuery and various new web standards..