There are a lot of things to consider when choosing a web hosting company. But one thing for sure is that price is no longer important. Web hosting is a very competitive field so the price just keeps getting lower and lower. It is so easy to find cheap web hosting for PHP and MySQL.
The important things to consider when choosing PHP and MySQL web hosting are :
For those of you who just want to experiment you can use MySQL PHP free hosting. There are probably hundreds of them out there, you just need to pick one. They usually place banners or other kinds of advertising on you web page and most are slow. Anyway you can't expect much from free services.
Actually even if you just experimenting with PHP and MySQL it's better to have you own web site. Free hosting usually have lots of restriction so you really can't do much experiment like opening a socket connection and stuff like that.
There's this one website that rank ten PHP MySQL website hosting company based on price, quality, performance and features. If you need a second opinion you can go there.
A bit off topic here. If you intend to build an e-business (for yourself or for a client) instead of just a website you should consider about Site Build It. It's an all-in-one site-building, site-hosting, and site-marketing service. It even outperformed Microsoft's bCentral and Yahoo Web Hosting Pro.
The only drawback is that the HTML templates provided look a bit lame. But since now you can upload your own template i guess it's not a big deal anymore.