Trying to know what buttons is best practice to have on the main start page for my game app. Is it good practice to have twitter/fb icon that takes user to those pages if clicked? And should I have a settings icon to allow user to turn music off/on in start page? I have that feature in pause menu but thats in game.

Put only the buttons the player needs, with buttons you need as second priority. Players want to start playing, so a Start Playing button is definitely needed. Beyond that, what buttons do you need? Music can be in the menu. If you want a menu button on the title screen, you can, but it's not essential. Social media buttons are fine, if you have a social media presence planned.