If you tune from E standard to C# you most likely have to get your guitar setup again for it to be any good to play due to the string being all loose. Might suggest thicked gauged strings as well (I use 11s on my main guitar, and I'm tuned to D standard).
What kind of guitar you have shouldn't have too much to say in the start, as long as it's equipped with some decent humbucker pickups. it's more important learning your way around the fretboard, as well as build a small arsenal of scales, chords and some basic music theory
When it comes to songchoices, just pick some of your favorite songs. They might be difficult to play, but they'll teach you a lot
One of the first songs I tried to learn was SIDstyler, which isn't too easy