Domain name for application? domainnameapp.com or getdomainname.com

Stay away from hyphens, people see them as SPAM domains.

I would also stay away from download (if you can). It's too long, and you might not always offer downloads in the future.

App to me sounds the most professional.

If you can, get both the get and app, and do some split tests.

Agree, stay away from the hyphens - looks cheap.

I would buy both domains, get... and ...app. See which one gets more traffic and then simply redirect one to the other.

Good Luck!

Check the search volume for the product you are selling. Use the google adwords keyword tool.

As I was just advising in other question:

drill down the Adwords Keyword tool data and get the domain name as exact match (no hyphen, no number, no trick) and DOTCOM. If you cannot afford it, then the keyword market is probably too competitive for you; find a niche that has some search volume: go down in the search volumes and make sure you get a perfact match dotcom.

example: if you sell shoes, get shoes.com if you cannot afford it, drill down find next top searched "shoes" keyword, say cool shoes, then see if you can afford coolshoes.com, etc.

Note that I wrote "afford" it. The domain might be registered... but available for sale. Check the website. If it's parked you might be able to buy it. Good domain names can be a great investment.