In Google's terminology, there are 2 terms. One is the landing page. It is the page which you got into through Google. Another one is the home page. That is mostly your index page or is the page you designed for people to start with.
What is the situation in your case ? Is landing page the same as the home page in your website ?
I personally think this is very very important if you want good conversion rates. Make sure that your incoming links has a fare share of home page link.
Sometimes that won't work. Especially when you are sharing article links than home page links.
It is easier to advertise content than the home page. What is the SEO element in it ?
One thing you can do is signature advertising using the home page. Then you can also do Adwords using the home page.
If you have optimised the home page, it is better that you work on making it the landing page.