Raspppoe is definitely the most stable and requires the least overhead for Win9x. It's just the "PPPoE'd" network protocols, bound to DUN.
Problem is it doesn't have the connection diagnostic functions that you mentioned. I got EnterNet 300 from telco when I got DSL, and it DOES have those diagnostic functions, but a price of a couple o' blue screens every day if used in Win9x

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I too got a router that could act as a PPPoE client, so thankfully that stuff is gone for me as well.
Xayd