To complete missions that require you to mow grass, you will of course need a mower. You shouldn't even bother with the cheapest version (Novacat 302 ED - 8300$) and buy FC 3525 F for 13 500$. This investment will pay off really quickly and thanks to the wider range of working of the second machine, you will complete tasks very fast (4 - 6 minutes maximum). The mower can be attached to the basic tractor.
After accepting a mission, drive the tractor with the mower to the right place (near field no. 36 or near the circus in the north-eastern part of Bjornholm map). Mowing is very easy- first, lower the machine [V], next, switch it on [B]. Try to mow by driving in circles. You don't have to be very accurate and such system will allow you to turn around quickly. If the mission doesn't end, you've probably left too much grass. You can either collect the grass or leave it. To complete this mission, you need the mower mentioned above. There's also a better model, but it's twice as expensive (FC 100300 - 52 000$). It was wider working width, but if you use a mower only for completing missions, you shouldn't waste money. The field you mow is not so big so the cheaper model will be enough.
Required equipment: a tractor (which you have from the start) + FC 3525 F mower for 13 500$.
Profitability: at early stage of the game, it is a great way of earning money, as you will earn back the money that you've invested after 2 - 3 missions.
Reward: about 5000$ + optional bonus (4000$ - 6000$).
Mowing is a great way for earning easy money, especially at the beginning of the gameplay - a mower is not so expensive and pays off almost immediately. If you've bought the best version for other purposes, then you can complete missions even at more advanced stages of the game - dealing with a small field will take you no more than three minutes.