Hello Abidon,

Welcome to TalkFreelance.

Unless the personal trainer is a celebrity coach, I wouldn't anticipate major traffic to the site, so a regular Linux shared hosting account would be more than plenty for your needs.

Yes, I would recommend an Australian-based provider due to faster connectivity/response time and speed with which the website is going to load for your target audience - Australian residents.

I am not sure how exactly you would like to setup your online store, but I would recommend to outsource the e-commerce part to hosted solutions that allow you to relax and focus on marketing and let them handle the payment processing part of your business.

Reliable domain registrars are: Namecheap.com, GoDaddy.com and enom.com that people tend to like the most.

It is hard to recommend a hosting provider without direct first hand experience (and I'd shy away from such recommendations). I suggest reading reviews and asking on web hosting forums such as HostingDiscussion.com and WebHostingTalk.com for advice.

Hope this helps a bit.