Winnie,
With caching (e.g. W3 Total Cache properly configured) -- good plugins -- and a CDN (e.g. MaxCDN or one provided by the host) -- shared hosting should handle thousands of hits a day, but if page speed is a concern, shared should not be in the picture at all.
There are several WordPress optimized hosts with prices across the board:
Nodeki in particular has some very affordable 'lifetime' plans that should out perform host gator (or other shared hosts) any day.
ZippyKid is cheaper per month and has a good rep.
I've had good luck with Synthesis and a mixed experience with WP Engine.
A dedicated server or VPS (unmanaged or even managed) is a big leap -- I'd avoid those unless you're really comfortable in WHM (Cpanel's big brother).
SInce cost is a factor, I'd develop on shared hosting then deploy to one the of options above for launch.
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Nick Ciske
@nciske