Your questions are very simple.
1, You can go to Australian Hosting Provider, but I believe their price will not cheap. Let's go to any Global Hosting Company which can offer US Server with cheaper price. Non-profit should be economic for first time start-up. I recommend it! Remember to find any hosting provider which has at least 1-2 years in hosting industry. Take a look into their domain whois and see creating date.
2, You should register domain name belongs with hosting company, because you will no need to manage DNS or make some changes if there is a same company. One contact for doing many requests will save your time.
3, Wanna discount? See hosting provider's Facebook or Twitter. They usually share promotion code on these social network.
Good luck, guys!