iOS software update for iPhone 3GS I have iPhone 3GS with iOS 4.2.1

I am having lot of issues in downloading apps from app store as most of the apps do not support this iOS version anymore.

There is an update for iOS 6.1.6 available on iTunes, will my phone get updated to this version and will I be able to download apps later, after the update.

My device is jailbroken because I see Cydia on it.

Will I still be able to update by restoring my iphone 3GS via iTunes.
Yes, you can restore your iPhone via iTunes. And because you have jailbroken your device it's the only way to do it.

Many apps are compatible with iOS 6, but I cannot guarantee you every app will work. This is because some new apps are only written for and compatible to iOS 7.