So you almost have a finished product, and don't have the money, nor the business expertise to go all out. First thing you need to do is analyze your own situation from business side.
Are you serious about turning this app into a business with revenue? If so, do you have a revenue generation model in the app? if so, you should approach target audience personally and based on the interest generated, use whatever means necessary to sell the product and generate income to sustain your servers. You might find this post by paul graham or this inc post, or this useful.
If your application involves certain amount of crowd sourcing, then you should definitely think long term, and get a business buddy of yours to join in to assist with the business building, or vc funding. Or otherwise, depending on your location, there are usually meetups related to startups you can attend in any given area, and get certain business folks interested in your idea for little performance based equity, or whatever setup you might see best.
Meeting the right people, and knowing what you want, can get you much further than google's app engine, Heroku, Microsoft Cloud, or Amazon Cloud services can. But, in case you would like to go solo on this, you might wanna read up on business stuff on places under ceoexpress and the likes.