List of Web Browsers For All Operating Systems
To browse most sites and also TLS 1.2 sites you'll need to use Opera 10.70 Build 3488 (for 95) or 12.02 (for 98 with Kernelex) (enable TLS 1.2 and disable anything older in Opera).
You'll possibly still need to use a proxy for ciphers and certs not supported by Opera but the TLS 1.2 sites I tried worked.
You can browse TLS 1.2 sites by using Retrozilla, K-Meleon (KernelEx) or Qtweb (Kernelex) but sites won't render correctly (Retrozilla) and you'll need to disable javascript for K-Meleon and Qtweb.
You can browse TLS 1.2 sites without worrying about the browser supporting TLS by using a proxy but most TLS 1.2 sites won't render correctly on browsers that aren't Opera, K-Meleon or QtWeb.
Probably best hope for 9x if relying on the installed browser to render is for someone to modify the leaked Presto Opera code or fix the Javascript issue in K-Meleon and Qtweb.
Web Render Proxy would be the next.