I've tried many apps, but LogMeIn(.com) is clear winner for me.
The extra value is that they switched from $50 app to the freemium model, so you can try the app for free and if you like the controls etc., you can upgrade to paid version and get features like HD video streaming or iOS styled user friendly file manager.
App Store - LogMeIn
Also, if you are willing to spend more money on the tablet, it's iPad all the way!
But if I were you, I would wait for late March/early April when the new iPad 3 is coming out. It is gonna have Retina 2048x1536 display in 10'' size (iPad 2 has only 1024x76
and also quad-core processor (iPad 2 and most of the Android tablets have dual cores).
I would wait also in the case that you don't want these new features, because with the iPad 3 on the market, the price of the iPad 2 will drop significantly...