Hi ! I think MOTO G is a good choice if your budget is around $200. If your budget is round about $100 then MOTO E is a pretty well choice.
If you have a budget of $300 then MOTO X 1st generation is awesome choice. Samsung phones are also good choice having different prices.
The SAMSUNG GALAXY S4 has a best Internet browsing and downloading fast speed and it has good features including WIFI, Bluetooth, 4G and Infrared port.
Moto G is also a good choice if you are in low budget. It also has many features and good browsing speed.
Moto G is an excellent phone for web browsing.
It won't use too much of your budget, and can do anything other higher-priced and 'better' phones can do at a lower price.
Its 1 GB RAM is more than enough for having other apps open while you're browsing.
So if you're downloading something and want to do something else (Youtube/Facebook), you can keep a tab on your download while doing other things and your phone shall still work at a good speed.