I hear the word budget and to me that means the John Deere1025 is out. I have a JD2025r and neither model is for folks on a tight budget.
I have 11 acres and got along just peachy with a 1998 John Deere 350 lawn tractor for the first 2 years. That thing is a mowing BEAST! Like you suggested, I have a little tow behind trailer, which is a 3 bushel bucket essentially. It is great for moving things, hauling branches, etc. A used quality John Deere lawn tractor is really worth every penny off of marketplace. We scoured for what we wanted and found one that was in great condition for $2k with a snow thrower attachment! It is versatile, small, easy to service and affordable. I mowed at least 5 of my 11 acres with it and it is still my “go to” for mowing even with the 2025r in my garage. Don’t get me wrong, love my 2025 but at $20k+ used I would not call it a budget machine.
Gook luck and enjoy your lovely new property!