Yes, as the others have said, very nice looking property. Depending on the texture of the lawn, you might want to consider a power unit pulling a gang mower.
On another thought, take a trip over to a nearby golf course that has similar terrain as you have. See what they are using and how it works out for them. (Ask the guys cutting the grass if what they have works good or if they would change anything. The boss might not know the whole story.) I would definitely have 2 or 3 actual candidates before you make a final decision. Then go to the dealers and ask for a "test drive" on your property. Should be no problem at all. Be sure to put the machines thru their paces. Keep in mind any attachments you might be considering in the future, such as a snow blower, tiller, etc.
Good Luck, and keep us updated with your search.