Most ancient art available today is in the form of pottery and sculpture, but some ancient frescoes and paintings on wood and ceramics still exist. A key element to remember when you imitate the painting style of ancient masters is that they often used egg temperas, not oil paint. Their paintings were typically flat in appearance, and blending colors was tricky. Furthermore, the subjects in ancient paintings were somewhat stylized.
To imitate ancient styles, pick a subject that is grounded in ancient mythology. Use a flat background, and create a stylized, almost cartoonish portrayal of your subjects.
Medieval art is nearly always religious in nature. Flat color still predominated because of the use of tempera paints and gold-leaf adornments. Linear perspective as it exists today was not discovered until the 15th century, so attempts to create depth and perspective were often distorted. Another quirky habit of medieval painters: They often proportioned children like small adults.
To imitate traditional medieval paintings, choose religious subjects. Paintings should be flat and somewhat stylized. Employ heavy use of symbolism.
During the renaissance, oil paints became standard. They allowed artists to blend colors easily and create natural-looking shadows. With the discovery of linear perspective, paintings became highly realistic. Subjects were often secular or taken from the mythology of antiquity. Renaissance art and baroque art are often similar in appearance, but baroque art tends to involve more artistic flourishes and embellishments.
To imitate renaissance and baroque painting styles, paint your subjects highly realistically, with accurate use of linear perspective. Oil paints on canvas are appropriate.