There's no shortage of great web browsers for Android, and which one you use is largely up to personal preference. If we had to pick one however, we still think Dolphin Browser is your best bet for speed, features, gestures, and add-ons.
Re: how to reinstall Google Play Store?
Lots of people pick up tablets and smartphones that don't have the Google Play Store pre-installed on them. Perhaps you've just granted yourself root access and accidentally deleted the Play Store, or flashed a custom ROM and don't want all of Google's...