There`s no simple answer to that. I guess all combined (except looks). I do root for all Slovenian players, but I admit that I would root for Dementjeva whenever she plays Slovenian one.
Some players have game that I like (A.Radwanska, Schnyder, Janković, Dementjeva, Hingis, Venus)- but I don`t root for all of them.
I like personality of some players (Dementjeva, Schnyder, Bartoli)
I`m fan of Russian language, music, novels, ... this means I would quite probably root for the Russian in almost any match.
I quite often root for underdogs. I like surprises (as long it`s not against one of my favorites, of course).
Well - my favorites are (except Slovenians who needn`t meet any conditions - it`s enough that we share nationality)
Dementjeva (like her game, her personality, her attitude, I start rooting for her when she was the most underestimated player on Tour, she was able to lose to anyone but also win to anyone. She got a bit of attention she deserves in the last few years - but she is still in shade of some other players)
Šarapova (actually I have no idea why I like her. Surely not because she`s pretty, because in my opinion Lena and many others are much prettier. I don`t like her game, I don`t like her personalitiy ... but I just have to admire her attitude and persistance in every match)
Schnyder (she`s pretty much controversial ... with her bad-mannered husband etc. ... but I find her very intelligent woman, and I like her game)
Zvonareva (I felt so sorry for her always when she used to cry on court ... I guess it`s my instinct to help and protect
And lately I also like her game ...)
Peer (when I saw her match against Serena in AO few years ago I started rooting for her. I just admired her attitude and fighting spirit ...)
Enough for your research?
(Apologizes for my English ... too lazy to check spellings now