I believe there are 3 types of field with each a type of improved soil version and a Paddy Field for Lotus.

You will need to harvest A LOT of crops in order to get the blueprint for the third one.

Grass counts as a crop when you want to unlock the next field type. You can sell it for 60 g each. It grows in 2 days and you can cut it EVERY day after the initial growth. You don't have to water it. If you don't have enough time to grow other things at the end of the month, you can grow grass if you have two days. The seeds cost 20g per bag. 40g turns into 480 when you cut down a field of 8.

The types of field are:

 - **Gravel Field:** You get this when you start. Requires 8 Soil to make
 
 - **Regular Field:** You get this blueprint at Rebecca's shop for 1600g after you've harvesting at least 300 crops. Requires 8 Soil and 5 Fodder to make

 - **Soil Field:** You can get this blueprint at Rebecca's shop for 2400g once you've harvested at least 1000 crops. Requires 8 Soil, 5 Fodder, and 5 Fertilizer. It grows crops a little bit faster here compared to the Regular Field
 
 - **Paddy Field:** You can get this blueprint for 3200g at Rebecca's shop after you reach the Summer of your first year. Requires 8 Soil and 5 Small Material Stone. This is used to grow Lotus, Rice, and Wasabi(!)

I found that the biggest advantage of the Regular and Soil Fields are that they allow you to continue to growing a previous season's crops for a few more days into the next season. 

A Regular Field will grow last season's crops until the 3rd day of the next season and the Soil Field will keep growing until the 7th day of the next season.