The reason they didn't go through Turkey and the Middle East is because Turkey wasn't an axis member and attacking through the Turkey would have just added another country onto the allies side. Also, the oilfields weren't the major target of the North African campaign. The major target would have been the Suez canal which, if it had been taken would have severed communications between Britain and her Far Eastern colonies, most notably India.

While modern history tends to make it seem likes the allies experienced defeat after defeat in the North African campaign the truth is the British absolutely mauled the Italians in North Africa at the start of the campaign. Which was unexpected consider how numerous the Italians were in comparison to the British. The Italians had 200,000 men against the British 63,000. The Italian offensive began when Italian marshal Graziani advanced into Egypt and camped at the small town of Sidi Barrani; the British counterattacked and sent the Italians back into Libya. Wavell in a brilliant move sent an armoured division into the desert and cut of the Italians capturing about 130,000 prisoners. The road to Tripoli was open, yet the British made a huge mistake. Churchill ordered many of Wavell's best units (the Anzacs, and other crack divisions) to Greece to help out the Greek army fighting the Italians. This left Wavell unable to continue the offensive. Now this wouldn't have been an issue, because the Italians were in no position to counterattack, had a German general named Erwin Rommel not arrived in Tripoli. Wavell's undermanned army was quickly sent packing into Egypt by Rommel. Had the British not pulled their troops back, the North African campaign would have been over in a few months.

Sources:

Second World War John Keegan

A World At Arms Gerhard Weinberg

The Fall of Mussolini, Italy, the Italians, and the second world war Philip Morgan