Where you host your website is a very important decision, for a number of different reasons:
Reliability
The site needs to be available for visiting spiders, in search of content. If the site is down when they arrive they cannot do their job and will leave. The spider may try again, but generally speaking 3 strikes and you're out.
Speed
If human visitors aren't served with pages reasonably swiftly, they will become dissatisfied and within a single click go elsewhere. Such is the fickleness of the internet, as online we are all spoilt for choice.
Neighborhood
If your website is located on a shared server, you are effectively sharing a house on the web with other anonymous digital neighbors. The cheaper the hosting packages unfortunately the rougher the neighborhood. Choose your neighborhood wisely, as you don't want some spammer next door on same IP address doing his best to consume all the server resources... and in the process get your legitimate website banned by association. Once you are blacklisted by Google you have to work to get back in.
Do...
research several hosting services - don't just go on price
check your your chosen host - ask them for customers and contact them for a reference
pick a host that can help you grow and scale if you are successful
Don't...
go for the cheapest - you get what you pay for and your customers won't thank you.