I think it is amazing how many replies she has received. I have seen others post similar questions and not get as many replies. Do not get me wrong I really do not mean anything. It is just an observation.
IMHO - a tractor in the 30 HP range would be good for the 15 acres. Use at least a 6' mower. I use to mow with a 7' and 45hp. But I bought an L2500 to have a FEL and get into tight area that the big IH could not get. I will miss the mowing capacity but no machine is perfect. If I could I would own one for every chore! If you do not need 4wd or the small size of the compact tractors. Take a look at a machine about the size of a Ford 2000 or 3000. Nice size machine for your mowing needs. They are a little bigger and heavier than a compact. Should be more stable on hills and can handle the mower size better.
Take a couple of afternoons and visit your local tractor dealers or private sales. Drive as many tractors as you can. See what features you like or dislike. Somethings I think are great features are: power steering, livew hydraulics, live PTO, shuttle shift - for a gear tractor, HST - some love it ( I do not care for the whine), ROPS-usally can be added to older tractors, lights, gas or diesel, ag tires - lots of traction (though they can damage your lawn).
A comfortable seat is important too. The old "pan" type on old tractors can be hard on the back.
Vintage tractors are great from the 60's and up. More tractor for less money.
Good luck!