You say your website is still growing. And, from your stats it seems you get quite some traffic. I wouldn't go with any normal shared hosting if I were you (not worth the risk of moving providers again). Maybe you can try semi-dedicated hosting before you get a VPS or a dedicated server.

Semi-dedicated hosting is the exact same thing as shared hosting. The only difference is that providers that offer semi-dedicated hosting only put very few accounts per server (10-25 instead of 100's like usually). This gives you alot more resources like CPU and RAM for your website, without having to manage a server or VPS yourself. It will be a bit more expensive than regular shared hosting but it will be less than a VPS or dedicated server.