My advice is for 3 acres, go pro with whatever you buy... buying cheap will cost you.
I'd say if you want some kind of tractor, it's almost impossible to justify a separate mower. You'd keep hours off the tractor, but it wouldn't make enough difference to justify it. I'd definitely chew that over before committing to a mower. I don't like mowing anything but open field with a tractor, but a mower makes an even worse tiller, snowblower, or loader when you need one.
If you don't want a real tractor, IMO anything but a ZTR, stander, or walk-behind is just silliness in almost every case. If it ain't got a 3-point and PTO there's next to nothing a tractor-shaped mower does that another mower can't, and it's nowhere near as good at... mowing. I was mowing with a 54" 4WS Kubota diesel hydro, and my Exmark walk-behind does a much better job in damn near half the time. Faster enough that I can mow my acre after getting home from work at 6:something except at the very end of the season, and free up my weekend.
If you don't have any steep slopes, check CL for an Exmark Vantage, Toro Grandstand, or Scag V-ride. All built like a masonry outhouse, but not very popular outside of the pros... I've seen some low-hour ones dumped relatively cheap by guys whose employees didn't end up liking them. Personally I like standing (admittedly I do it for <2 hours, not all day) better than sitting on a ZTR, and you can get in tighter/farther under trees. I got a 2-caster sulky for my mower to turn it into a kinda-sorta stander tjat can still do steep spots.