My opinion.
Lets break it down. You plan to have 3 ac in pasture. While you could mow this with a lawnmower, it will be a LONG process.. and will wear the poor thing out. Maybee a lawnmower pulling a drag mower.... but then we are getting expensive.. and they are dedicated machines.
(<font color=red>cheesy salesperson voice
n ) <font color=green>You need a tractor!<font color=black>
In all seriousness though, you sound like a prime example of a small utility tractor. Your uses will dictate the price you need to pay. 2wd vs. 4wd, gear or hst, etc. If only mowing, no front end loader, etc... you may get buy with an older model.. like a working antique ( like a ford 8N or NAA ( insert <font color=blue>shameless plug-I own an 8N)<font color=black>.And depending on where you are.. these can be anywhere from 1k and up.
If you need a loader.. I would look newer.
For instance.. there are 5 tractors in my local paper today.. a ford 8n, a ford 3000 a ford 5000.. all are 5k or less.. and the ford 3000 has a loader.. and is quite a bit of tractor.
There are also new alternatives, like jinma series of chinese tractor... A 2wd 20 hp would be in your range, and it would be new.
Other great tractors like any of the 'big 3 ' or even Yanmar.. I paid 3k for my 1700 and have worked the snot out of it.
The new / used will depend on how you feel about occasionally turning a wrench, or other small maintenance issues.
There is a wealth of knowledge from the users here. If you have any specific questions, ask away and we will try our best to bounce answer off of you!
Soundguy