I use a matt screen protector which has helped me many times and the Apple smart cover.
For applications, I suggest that you decide on your own depending on the reason why you purchased it.
I use my iPad for -
Browsing Internet on the go - Safari and Mail
Remote control for my music system - Music Fidelity controller and Linn Kinsky
Reading PDF books - Kindle app and Adobe PDF
For occasional chat - Skype
Finance and news - MoneyControl, NDTV, Safari
For jotting down and discussing ideas - PlainText, Bamboo paper, classic board
For documents on desktop and iPad - Dropbox, iKeePass.
IPad store has a lot to offer. Decide for yourself what you need.
If you bought the iPad without a purpose then enjoy your new toy.