Your snippet call on your home page is correct:
[!AjaxSearch? &ajaxSearch=`0` &landingPage=`37` &whereSearch=`content`!]
But on your landing page you should use:
[!AjaxSearch? &ajaxSearch=`0` &whereSearch=`content` &showInputForm=`0`!]
You should keep the non-ajax mode on the landing page.
By choosing &whereSearch=`content`, you exclude the search in TVs. (the default value is `content|tv`)
By adding: &showInputForm=`0`, you don’t display the input form on the landinPage (#37).
The nearest demo is:
AjaxSearch » Demos » Ajaxsearch 1.9.0 Beta » Non-ajax mode » With a landing page
On this demo, I use [!AjaxSearch? &ajaxSearch=`0` &landingPage=`[[GetFirstChild]]`!] on the first page(#38) and the landing page is the first document child (#39)