Hi Sara,
A URL is unlikely to ever bring down a penalty on its own - there would need to be a lot more at play before this happens.
Try not to get too hung up on which URL for SEO purposes, but do look at the one that is going to serve you best in the years to come. If the business is an app, then having app in there can help others understand what it is that you do.
Try to focus on the brand as well - if you market yourselves as mobilewebapp, then try and stick to something close that will again help with brand recognition.
You will be surprised just how much Google loves a brand, so choose wisely and market accordingly.
-Andy
