It is understandable that you’d like to cut down expenses. Saving expenses at the cost of risking your potential to be found online doesn’t seem to be a very wise idea.
Instead of cheaper web hosting solutions that might save you some money, they also come with their own problems that search engines do not like. Most of them have infrastructure that slow down your website. Having a slow website will greatly diminish your chances of ranking above your competitors.
A lot of these cheap, inexpensive website hosts do not offer your website an SSL certificate – a small but very important ranking factor according to Google. It will mean that your website will be labeled “Not secure” when someone visits your website. Search engines do not like unsecured websites and your ranking factor will be diminished.