I use Logmein too. The IOS app is called Ignition. Very good in general. Only problem is when my machine at work crashes - you can’t remote boot my machine (I think I spec’d the wrong CPU or something?!?)
I used to use iTeleport because it handled 2560x1600 very smoothly, but with dynamic IP it takes a lot of fiddling to get it to work. So I now use Teamviewer, which is flawless, really. Very solid, quite fast and handles the high res with ease.