The frustrating part is that there are so many variations to consider.
- Is this a new site being built from scratch?
The first thing to remember is that it is easy to move a "young" website from one host to another.
- I've successfully used a plugin that creates a backup file, then downloads the file to my local computer.
- Next, at the new host, I created a fresh/clean WordPress installation
- At the WordPress site I installed only the one plugin, then launched it.
- The plugin asked me to upload the file from my local PC and the plugin did its magic
- After it was installed, I was logged out and had to log back in with the admin account from the old site.
The bottom line is that it is easy to recover from an early bad decision.
Next, try to use a hosting provider different from where you registered your domain name.
Google ranks how quickly a site downloads in it's search engine results, so eventually speed will become an issue. The discussion around that is how much you intended to rely on Google to bring you customers.