The cheapest (and perhaps the easiest too) way is:
Subscribe to Apple's enterprise developer program: $299.
Develop your app. Hard to say how much that might cost in terms of your time, but the amount that you have to justify to the purchasing folks is $0.
Stick your app on a web page. The page can be simple or fancy, but to keep on Apple's good side it should be a page that's only accessible to people in your enterprise. Cost: $0.
Any way you slice it, you'll need an enterprise license, so the $299 is non-negotiable. (Unless you want to try to make due with ad hoc distribution. The whole ad hoc thing is really meant for testing, not for product distribution, and just managing it will cost you a lot more in time than the price difference between the standard and enterprise program subscriptions.) There's more that you can do, such as using MDM to install your app(s) automatically on all the devices that you manage, or creating an "app store" that hosts all your apps. Whether these things make sense for you depends a lot on your circumstances. In general, I think you'll know it when you've reached a point where going with a third party service is going to make sense for you. Keep it simple for now and move up to something fancier when you have a real problem.