Beit Alpha is a medium sized sweet burpless Lebanese type Cucumber. It has green, straight fruit growing to 15cm long. They have high yields and a good shelf life.
Image: (of Cucumbers lying on the ground...hmmm)
Rasbak at Dutch Wikipedia [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia Commons
Cucumber Lebanese 'Beit Alpha'
Cucumbers like rich well drained soil with a pH of 6.5. Mulch them well (straw is great) and avoid overhead watering - wet leaves cause Powdery Mildew.
Give them plenty of sun and (if you can) something to scramble over, like a trellis, to prevent them lying on the ground for slugs and snails to find.