There is 2 versions of LogMeIn.
A free version (which works great for most people.)
And a paid version which allows you do do more. (print, file transfer, stream.)
Its also as good as your internet connection on both end. If your Ipad/Iphone have a fast connection and the computer you are controlling is on a fast connection. It's pretty good, there will always be a slight lag though.
I'd recommend trying out LogMeIn between two computers first and see if you like it. (That wont cost anything.) If its acceptable , then buy the app.
I personally like it and have the app.