What are the best hosting which allow you to install Magento in few clicks with a low cost?

Magento has a page in their Wiki with providers that offer free Magento installation, check that out.

Are you looking for australian hosts?

Try Crucial Web Hosting, sorry can't post any links yet o_O

crucialwebhost.com/blog/announcing-magento-one-click-installer/

Also, with SSH access, you can easily install Magento without much trouble. Just head over to the Magento downloads page and they have various guides to help you out.