A couple of options:
1) Go with a small, economical garden tractor for your "finish mowing" (lawn) work and then get a tractor for your field mowing (either with a larger finish mower or rotary cutter). In this case something like a 100 series would be good up to a few acres, and as for the kind of tractor, it would depend on the size of your fields. Anything from an older compact tractor to an old vintage 8N or something like that.
2) Get one machine to do both jobs. In my opinion, when you're in the price range of an x300, for a couple thousand $ more you can go up to a subcompact like a 2305, which will give you the next jump in terms of power, weight, and 3-point hitch/PTO capabilities. Plus it will open up a lot of other implement possibilities.
That said, plenty of people use their garden tractors to mow fields, so long as the field is in good shape.
How much lawn and how much field do you have?