Switching web hosts will not affect your web site ranking in any way.
There is only one thing that you should take into consideration. When
you change your domain's DNS by pointing it from one server to another,
there is a propagation period before the new changes take effect. You
should not bring the old website down until you are 100% sure that
search engine crawlers are already indexing your website on the new
server. A safe course of action would be to:
1. Migrate your web site along with all the content and data to the new
server.
2. Change the primary domain name's DNS to point to the new server.
3. Observe the new server log for visits from search engine crawler
bots.
4. When you notice that the search engine crawlers are indexing the web
site on the new server, it is safe to bring the old one down.
