So I started a classic game without the tutorial. Mission one - two casualties. Mission two with a small UFO taken down - complete failure, first three of my squadmembers were obliterated by sectoids, then this energy guy flanked and murdered the fourth one. I'm completely hooked; probably will restart on normal to get a hang of the game and learn some nifty tricks and then restart on classic once I feel ready.
This is about my experience too. I found that sometimes the tactical bits on classic would be alright and other missions would be a total clusterfuck. What really screwed me though was running out of money to provide proper coverage in classic since the game's economy is different than the original's in a lot of ways. I bumped down to normal for a bit mainly to get a hang of base finances. Thing is, even with ironman on, normal is pretty easy.
I'm surprised that I like this game as much as I do. There are things that I miss from the originals (well I mostly just played TFTD) but this one seems solid in its own right so far.