Well, as for the shared hosting, if they can't handle 2000 hits a day, then they deserve to be brought down. That's not a lot of traffic. But if you really are worried, a VPS should be enough. And if you really think it's going to grow, you can get a fully dedicated server. I doubt you'd need a fully dedicated server.
As for split-testing pages, that could get complicated. You'd have to track statistics like how many people visited a blue page, how many visited a red page, how long they stayed, how many links were followed, whether they went inactive (meaning they're looking at another site, away from the computer, etc.) or they were active the whole time. It can be very very complex. Not to mention once you get all the data back and recorded, you'd have to provide them some sort of analysis mechanism (graphs, raw-data export options) so that they can run analysis on the data themselves (regressions and statistical errors etc.).