God bless your search for Truth!
The link that Scamandrius kindly provided contains, essentially, all of the prayers that are in my little "Molytovnyk" (a prayer book), printed by the Ukrainian Orthodox Church of the USA. I have acquired the habit of saying these prayers quickly (aloud, although not loudly, but also not quite whispering) in front of the Holy Icons of our Savior, the Most Holy Theotokos, and my patron saint (St. George the Dragon Slayer), every evening and morning.
Informal prayers - or improvised prayers, I am not sure which term is better - can certainly be added to these. My "Molytovnyk" says that in the morning, one possible time to add your own personal "informal" or "improvised" prayers is right after the Remenberance (i.e. after the part when you pray for the Church, for the civil authorities, for your spiritual Father, for your parents, friends, the old, the young, the poor, etc., and before you pray for the departed). In the evening, it's after the prayer to your patron saint and before the Kontakion to the Most Holy Theotokos.
Before meals, the Molytovnyk suggests "Our Father" and the following quick prayer: "Lord Jesus Christ, Son of God, you blessed the food of your disciples; bless also this food, for we believe in you, we have hope in you, we pray to you and we glorify you, to the ages of ages, amen."
Also, there is this simpliest and shortest and most wonderful of all prayers, the Jesus prayer: "Lord Jesus Christ, Son of God, have mercy on me, a sinner." The Orthodox are encouraged to learn to say this prayer continuously, and especially when you experience any difficulties, struggle, turmoil, anger, frustration, envy, or any of the so-called "passions."