You can look up the lives of saints at http://saints.sqpn.com/
The Blessed Virgin is considered to be the most powerful intercessor.
You can pray for certain problems to saints who are known for specific intercessions. Like if you lose something, you can pray to St Anthony, if you are suffering mental/emotional problems, St Gemma Galgani is a good saint to pray for. If you want to perfect yourself in loving God in the little things you do, pray to St Therese. For purity, you can pray to Mary, Joseph, St Augustin, and many more. For souls in purgatory, and if you are devoted to Divine Mercy, St Faustina is a good choice. For conversion of souls, pray to St Monica. For persecution, to any of the martyrs and apostles that you like.
My favourite saints are St Therese, St Rose of Lime, St Rose of Viterbo, St John the Beloved (especially because he was so close to Christ).
Read about saints. Those you feel that you feel a connection to, pray to them.