If you're going to brew a true Oktoberfest using a lager yeast, 60°F would probably produce some fruitiness from esters or other noticeable off-flavors. You really need to be colder than that... more like 50°F. Then for lagering, it's best down to about 33°F. If you can get those temps, you're golden.
What yeast do you plan on using? For ease of use (dry yeast), I can recommend Saflager W-34/70 (minimum of 2 packets, rehydrated, for ~5 gallons).