"What is critical" depends on your marketing strategy, those you serve best (your target) and where they "hang".
I don't know if you remember when the MagicJack Inventor started selling his new product (that people laughed at). He had a one page website.
The one page - with a video
- what it is
- how it works
- the why its important
- who you are
- who you sell to (who loves the app)
- what people get when they buy (benefits)
- how to buy (more than one option)
- how much it cost, (maybe a comparison to others?)
- why they should feel confident (guarantee)
- who said awesome things (testimonials and press),
- Blog - for rants, raves, notifications, news, updates, inspiration, success stories, SEO - getting found.
Many have moved to using templates which have pre-planned pages and people fill in the pages because they exist in the template. But the templates miss the small pieces that create an "aura" which supports belief (not just understanding).
Maybe a different way to approach it - at the moment where people are asked to say "yes", is there ARUBA - no, not like the song. :)
Attention - do you really have it?
Relevant - does it show relevance?
Understand - can they "get it" in an instant?
Belief - will they believe based on the info provided?
Action - will they believe enough to take action with a "yes"
When you look at an Amazon product page, there are many of the same elements.
If the primary yes page is on iTunes and Google Play, etc, then your website will offer something more than the app page. Something to inspire and help them believe "this is perfect" and confirm you are not a kid working in their parents basement. :)
Those are the notes off the top of my head.
If you haven't heard of MagicJack, here is where you can see a history of their website. (which is no longer the simple website as when he started)
And there will be privacy, FAQ, disclaimers and other legal notices that your attorney will say must be included somewhere. :)