Ping has little bearing on how fast a website loads. Throughput is more important in such cases, so try to do a test download of a large file. If you get good speeds, and hopefully maximize your download speed, then you'll be in good shape. You should be able to do that with any ping in the double digits (<100ms). Once you start going above 100ms, then it becomes harder to do good throughput as the packet sends and ack's take longer to go back and forth.
The ping latency will essentially tell you how fast a packet goes from the server back to you. This is solely dependent on the route between you and the server. If you get very low latency, this is indicative of proximity and/or good peering from the network. That said, sometimes you could be physically close to the server, but the route will take a roundabout way to get to the server, giving you a higher latency than you should.
With CloudFlare, I am not sure if pinging will give you latency to CloudFlare or to the actual server. It is possible that true latency is higher since you may not be measuring the path between CloudFlare and your server.
