Bit of a rant here but I host a site with one of the largest known hosting companies in the world - especially the USA. As this particular blog has grown we have absolutely outgrown our current (terrible) hosting.
We are currently on the cheapest and crappest hosting package, its like 6 bucks a month, and 100% you get what you pay for.
I'm not asking - I'm telling you - do not host on a crap server if you are serious about SEO. Page times are slower to load meaning that visitors get impatient, its a headache to update pages, blog maintenance etc - just dont do it.
Cant wait to move away from the hositng I'm on. Thing is though that the hosting package is great for a little site not doing much - but if your serious about your business your server needs to be able to process page requests FAST and not cram 4,000 domains all on the same server rack and IP address.
You get what you pay for. Its a bit like flying in Economy or Coach. Don't expect Canadian Salomon, Polish Vodka and Caviar.
Rant over. Time to move hosts and make some more dough.
And yes, I know - CDN, compression, using LESS, using limited plugins, etc etc yadda yadda all helps - but what helps the most is the actual hardware your operations are sat on. Period.