what stuck out was 1 acre, and lots of trees. and turning, and mowing.
i would say zero turn mower is were you want to go. vs a generic riding lawn mower. so you can make sharper turns. the deck is out in front of you making it easier to see were deck is to get around stuff.
zero turns have different control types, from lever per hand, joystick per hand, single joystick, steering wheel, to foot peddles.
due to 1 acre size, you really do not have enough acreage to justify a larger zero turn mower / commerical mower. and in that deck height might be an issue for you. more so if grass growth can get away from you... (vacations, long wet rainy portions of spring, just busy with everything else in life (kids/famialy)). with that said zero turn mowers the cheaper smaller size ones, the deck height may not lift up as high as a riding lawn mower.
tend to see more folks complain about 2 lever setups (one lever per hand) to control zero turns. due to arms are being held out from body during entire time mowing. and there job / regular life does not really encourage muscles that have your arms sticking out for longer periods of time.
myself, hate old tractors and even manual trucks, were you had to constantly push in clutch to change a gear. or turn on/off PTO / mower deck. my foot from toes, to bottom arch of foot just "ached" and felt bruised. and pending on how i sat, ankles would hurt. more so if i wore boots or high top shoes for past week, were shoe laces were tight causing little ankle movement. (ankle muscles got weak).