Test internet connection details

hi,

I just subscribed to new provider, some VDSL that also carries video for my tv along with internet, and started having problem with it, though speed test produced good results:
down: 6 Mb/s,
up: 4 Mb/s,
ping 83 ms.
I also see that after starting test it thinks for a while and then gauge jumps to 10 Mb/s area, so 6 Mbs could be average. But response with loading sites (even local) very bad, both on cable and thru wi-fi. My set up includes connection from phone jack to some gateway router which also provides wi-fi. Brand : <Cell Pipe 7130 Residential Gateway>

Does ping time matters? I've checked on some public wi-fi that work very faste and see ping time 11 ms though with 3Mbs up speed.
What other params and how I can check for internet connection, so I can start talking with these guys.

They BTW are Smart Consolidated Solution which have very bad yelp score.

Tx to all
D