You might want to take a look: Mauro Giuliani wrote a set of 120 arpeggio patterns that he included in his "Method".
Basically, they are Right Hand patterns meant to be played over simple chord progressions.
I dont have the book in front of me, but it is included in Giuliani's Complete Studies published by Tecla. There are numerous other versions floating around too...it should be very easy to find.
Obviously, there are far more than 120 patterns you could play, but this might give you some ideas for inventing your own.
They are also pretty good agility exercises and warm-ups.
PS. And why wouldn't it be "Classical"? This doesn't get mentioned often, but guitars do an awful lot of accompanying; knowing some arpeggio patterns can be very useful, especially for a composer!
2015 John H. Dick
1994 Larry Breslin ("Deerhead")
1952 Vincente Tatay