As a first time tech entrepreneur, I was confused if I should select one tool for mobile prototyping and other tools for implementation. I wanted to deliver my mobile app service as soon possible but I don't want to make mistakes when selecting tools. I have seen tools like Appcelerator, https://codiqa.com/ and PhoneGapp. Other than that should I also develop for android and iPhone separately, or should I use one of the above tools to develop once and deploy in different devices? Time and money is also a constraint for my startup. Please advice me. Thanks.
Just looked at Flinto suggested by Dan, seems a great tool indeed.
I previously used Proto.io, which offers similar capabilities / user testing of a "fake but looking real" app.
Whatever, I highly recommend you to read http://svpg.com/flavors-of-prototypes/, because it just seems there's confusion in what you aim to do with your proto. Regarding the frameworks you mentioned, it seems you're looking to build a MVP / live data prototype, whereas most answers (mine included) gave advice for low-qual or a high quality user prototype.
Also, for the backend stuff, I advise you to have a glance at MBaaS (Mobile Backend As A Service) like Stackmob or Parse.
Hope it helps!