You can't actually rely on styles getting inherited, which means you will have to apply every single style to every single element all the time... This means the font-size on the div won't actually have any effect on the text within it.
For a quick fix I suggest wrapping the text in a paragraph and applying the needed styles to it.
<div style="padding-top:15px; font-size:12px; color:#363636;">
<p style="font-family: 'Helvetica Neue Light', 'HelveticaNeue-Light', 'Helvetica Neue', Arial; font-weight: normal; font-size: 26px; line-height: 36px;">Thanks for downloading our app. Prepare to experience a new world of imagination. Check us out on <a style="text-decoration: none;" href="https://www.facebook.com/myApp" target="_blank">Facebook</a>, <a style="text-decoration: none;" href="https://twitter.com/myApp" target="_blank">Twitter</a>, and <a style="text-decoration: none;" href="https://plus.google.com/+myApp/posts" target="_blank">Google +</a> for the latest details. Oh, and tell your friends!</p>
</div>
Generally I would advise writing the styles in a style tag and then using a service like http://inliner.cm when you're finished and ready to inline the styles for gmail support. That way you won't have to copy&paste the font-family and default styles everywhere yourself
Using the suggested method of styling your html email in a <style>
tag in the head and then using an inliner, you can actually go back to using the ink framework too and still have it work in gmail.