I've built a load of apps over the years and tried out many of the major providers. Currently I'm the CEO of a startup making advanced email technology, which is incredibly server intensive, so I feel I'm in a good position to advise!

I'm not sure from your question if you're looking to host the backend or frontend of your mobile app, but what I have to say applies to both really.

I'm going to assume that you're not a systems administrator, and have no desire to be, so I think that rules out self-hosting and colocation. That's when you buy servers to run yourself or rent server space in a shared facility. You'd need to spend a lot of time maintaining these servers, fixing bugs, etc. and it's basically a full time job.

Next up we have the option of renting space on shared servers. You can get instances on Amazon EC2 or Rackspace fairly cheaply, and you'll be able to start out with a default configuration that has an operating system loaded for you already. You'll still have to maintain these though, and the way I look at it, do you really want to be responsible for installing updates and 0-days on a server if you're at an important event, or in the middle of something? I sure don't.

Then we get down to PaaS (Platform as a Service) offerings like Amazon Elastic Beanstalk and Heroku. You'll rent small amounts of scalable space from them which you can increase or decrease at any time. So if you get a spike in traffic, you're covered. You'll get more transparent pricing, more support, and you're not responsible for updates and server maintenance. You get less control of the stack this way (for instance, it's more difficult to install custom packages) but it's far less admin than any of the previous options.

This is where I think you're at, and having used the two I think you'd be best off with Heroku. They have good and bad points (doesn't everyone) but I've been using them for some time now and haven't had any major problems. Deploying code is a couple of lines in a terminal - it's super easy. And maintenance is all taken care of for you.

Some companies have taken PaaS to the next level and just provide you with an API and a nice web interface to interact with them, like Parse. You can host Javascript on Parse, but not PHP, so it's not a good fit for you.

There's other cheaper options too, like shared hosting. As you're using PHP you could host on the majority of web hosts (1and1, Hostgator, etc.). This is a terrible idea, and you shouldn't do it. You'll hit memory limits and other nasties really quickly, and you'll not get the developer support you need.

There's a ton of other hosting companies out there that I didn't mention, and it's a massive topic. You'll also need to think about databases and storage, and who's going to manage the deployment of code.

I'd love to talk to you more about this. Schedule a call if you have any other questions, or if I can explain anything more thoroughly for you.