what mean local caching in hostogator

You'd really have to ask them... it could be something like memcached, Redis cache or simply caching files to SSD (most likely not). Frequently HostGator uses "buzz" words for their advertising/info pages. Like their unlimited stuff... nobody can really afford to give unlimited (especially file space). In fact, if I remember, they had a limit on the inodes when I was using them ages ago - and they also limited the concurrent mySQL connections to 25. If you exceeded that frequently then they "encouraged" you to go to a larger plan. I did - a VPS with another company and then shortly later dedicated servers.
 
First thing before anyone can give you a recommendation is where is your target audience.
I'd also suggest going to WebHostingTalk and reading the reviews there of various shared hosting providers.
 
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