All depends upon how many obstacles & what space you have between them,
An old commercial with a big deck 60" to 90" will serve you better but of course you need a big trailer to move it from one property to another.
I see a lot of really cheap Great Danes out there with 61" decks that would suit you fine.
Two older, cheaper mowers are always better than one new expensive mower and if it is an old tired mower then no need to keep it under cover , just a small one over the engine will be fine.
My landlord sits on 1000 acres , around 600 of these are pasture that require regular mowing after the cattle have finished eating the grass to knock down the weeds
He uses 3 2000 series Cub Cadets with 48" & 54" decks and it takes all 3 of us 6 days of full on hard yakka to knock it over
He also has a 1962 40Hp Inter with a 10' flail mower that will do the whole pasture in 3 days that we use for heading the seeds in fall because the mowers can not cut high enough to leave feed for the cattle.
For the paddocks with a lot of Tussock grass then there is another , slightly newer Inter ( 1968 ) with a 10' slasher on the back.
Old small farm tractors are a dime a dozen over here and I would imagine it would be the same 10 fold in the USA as cost pressures have forced small farms to combine into big farms with corresponding big farm equipment.
So as others have suggested look at some big equipment for the broad acre stretches and use the little stuff for trimming around the fence line.
If the ground is fairly well level the look to old fariway mowers retired from golf courses when you can get 12' to 20' cut in a single pass.
Cutting a wide swathe slowly will do a better job and is better for the grass than trying to race over the 10 acres quickly .
And go for something with a fabricated deck
