I need to estimate network connectivity of various dedicated server hosting providers, e.g. how fast and uniform will my services perform when hosted there. I use traceroute command on my home computer to check the servers that are hosted by the provider; if I don't know any, then I traceroute their homepage (I know it might not be on the same network; it's a guess)
Intuitively I aim for:
- minimum number of hops,
- minimum roundtrip time both for the target and intermediate nodes,
- and lack of stars:

Are all these metrics relevant for general web service hosting? What do stars mean and should I really avoid them?