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.
There are many different approaches with prototyping, and it really depends on who you have involved with your team. If there is someone that knows Adobe tools well, there's nothing wrong with doing it in Illustrator or Photoshop. Other alternatives:
Keynote (there are good templates available)
Personally, since I know Xcode well, I now prefer to make a functional prototype on the device itself (with fake data, etc) because with iOS7 the feel and motion of the app has become much more important. This is hard to convey through material on a desktop and laptop, and even being able to touch and swipe on the device itself irons out problems very early on. Touch zones are also important for user interaction, which isn't always apparent until users interact with it.
The bar for the app experience has increased dramatically, so be careful smashing something together in one of the cross-platform tools. This is especially important when going to multiple types of devices because the user expectations are different.
All that said, if the interface is fairly simple, definitely go for a cross-platform solution! Be happy to go more into detail with your specific app idea.