Rare's games on N64 were second-party. At that point, Nintendo owned 49% of Rare and funded and published their projects. There are some great third-party N64 games, though, from Konami, Enix, Hudson, etc. It's a shame third-party N64 games so often get overlooked.
Third-party support is important to a system's success but not the be-all and end-all. For example, the Wii was a massive success, and, yes, it had tons of third-party releases. But a massive amount of its third-party releases are shovelware, and Wii players are often hard-pressed to think of many third-party Wii games they really like. Despite the availability of third-party Wii games, a lot of people bought the system just for the first-party offerings.