You will need:
- A mid to high-end Android phone running Android 4.4 (kit kat) and above is recommended, which is able to access Google Play and Google Play Services. You can check what version of Android your phone is using by pressing Applications -> Settings -> About Phone -> Firmware version.
- Your phone must include GPS and location service capabilities. Some low end phones such as the Samsung Galaxy Star Pro do not include a GPS chipset.
- Stick with with major manufacturers, and stay away from the bottom-end of any manufacturer's range. Brands like: Google Nexus, Motorola, LG, HTC, Huawei, Samsung, Sony, Asus are usually fine. Devices like: Galaxy S5 or S6, Galaxy Note 4 or 5, Nexus 5x or 6, Motorola Moto G or Moto G2 (good budget options), Moto X, Moto X2, HTC M9, HTC Desire 610, Azus Zenfone 2, Sony Xperia Z series.
- We can't give an exhaustive list unfortunately, but in general if the phone is handed out free with a $10/month plan, or is only available from one carrier in one country, or doesn't have product support pages in English, it's probably not going to be great. If the manufacturer lists it on the front page of their website, or positions it in the mid-high range, it'll probably be good.
- A Google account signed in on your phone. If you have multiple Google accounts attached to your phone, the first one will be used to access the Market.