I'm wondering if replacing a squid proxy server for a heterogeneous network that permits traffic by IP addresses by one that authenticates usernames is viable, having in mind all those different softwares out there that may or may not work OK with authentication. What are your experiences? Am I asking for troubles?
Depends on the software, and the authentication, and how much pain your users are willing to eat.
I am assuming it's traditional, rather than transparent proxy. Adding authentication to a transparent proxy is harder.
If you enable "proxy auth", everyone will get a popup for each browsing session. This will irritate some users, encourage others to save their password (may be a problem, maybe not) but on the other hand, most software will let you put authentication in. You will find things "just don't work" and you will spend a few weeks helping users add auth to software that likes to have its own proxy settings. Most stuff will eventually play ball though. It's not hugely painful, and the benefits of having auth can be worth it.
You could use NTLM or Kerberos, but you say your network is heterogeneous, so its unlikely (m)any of your machines are on a domain, so the "SSO" advantages are likely to be few.
There are other options, like captive portal, but this is harder to implement.