is Submitting Landing page URL directly to google is proper way to get indexed quickly or we rely a high page rank website to link back so that google's spider detect it and indexed it .. Which one is quicker???
You just need to take care f your website content and its design. If they are good enough, you are going to index faster.
I do not think there is a quick way to get indexed in Google, except of course when it comes to white-hat SEO techniques and high quality content on your site. Sure there are unethical things that can probably get you indexed faster BUT it will eventually catch up and result in dire consequences.
If your site is new, then there's no need to worry, just make sure that your site has fresh, and relevant and quality contents.
Simply keep everything clean, make sure you add your meta tags correctly, fresh content, and manually adding your URL to the google indexing isnt a bad idea either.
both are the good ones... but i prefer to go for the 2nd one i.e. to link to get a link back from the high pr sites its natural and more effective... also try to maintain keyword-enriched content and meta tags for the page as well