Here are some considerations when choosing your hosting company
You get what you pay for and ensure you are paying for support. Make sure you look for 24hr support. I have had a case in the past where a site has gone down and the host company did not notice it then or in the morning. It took about 16 hours to notify them and get back online.
Things break and you need a friendly host (speaks English as well as digital) that is keen to help you. Remember your web developer (thats me) will not be around at 3:00am before that important client will be looking at your site or you have been featured on TV.
How much data can you store and serve from your website and downloads.
If you think you will get hit with sudden traffic (you are featured on TV) ensure your site will scale up with the traffic. Your host should be able explain what this means.
If you are running more than one site, you will save money by buying a “reseller” or similar setup. In this context, the host charges you total data and bandwidth costs and you can add as many domains that will fit within these limits.
Ensure that the host allocates enough resources. A lot of hosts will oversell resources (too many sites on a server machine) which makes your site run slow, especially if another site on the server gets hit with heavy traffic.
Processor + Ram
Make sure you choose Linux hosting. Linux works better with open source software such as WordPress and you don’t have to pay additional Microsoft taxes and fees.
If your target audience is Australian, then I recommend a hosting solution physically located in Australia. This means slightly faster speeds, especially in peak times (specifically peak times in the country where the server is located). It also means support during Australian business hours.
If your target audience is global, I recommend hosting in the USA as it is a lot cheaper and they are the central hub of the global internet.
Caching solutions such as cloudflare can offset an issues with location of servers as they have multiple servers and serve from local location.
If you site is pushing the law such as a campaign site against a specific company with a large legal team etc, then have a plan B to offshore it out of Australian (and US) legal jurisdiction. Places such as Holland and Iceland might be a good place to start looking.