The Shulchan Aruch (the Halachic Authority of the Sefardim), Orach Chaim 260, states that one should begin cutting the nails on the index finger of the right hand and the correct order is finger number 2, number 4, number 1, number 3 and then number 5. On the left hand one begins with the fourth finger, and the order is 4,2,5,3,1. The Remah (the Halachic Authority of the Ashkenazim) rules that one starts with the left hand. As far as I am aware the Halacha is the same for both fingernails and toenails.
According to the Mishna Berura, sk 6, one should be careful not to cut fingernails and toenails on the same day. On the other hand, the Sha'arei Teshuva rules that one does not have to be concerned as the AriZ"l was not. I asked a Sefardi posek and he said that there are Sefardim who are careful about this and those who are not.