Bernie is right. A systematic subsurface drainage system for 60 acres would be expensive. Depending on the soil type and crop uses, most tile systems have the tile placed 40 feet apart. Looking at my old drainage guide, that is 1,089 feet per acre, times 60 is 65,340 feet of 4 inch tile (plus a main or two). For legume hay crops such as alfalfa and clover, that is usually the recommended spacing.
In the states, we have county soil and water conservation districts that will give recommendations on what would be best for a farm field. Not sure if the Canadian Natural Resources Ministry or if you have an Agriculture Ministry that would take a look at your farm for you.
Many of the tile contractors are experienced enough to lay out a subsurface system themselves, especially now with lasers. Wheel machines and tile plows are usually used to put in the system, then there is the connections of the main tile and the laterals, and such. Haven't kept up with pricing lately.
Eastern Ohio is more expensive than most of Western Ohio. Simply, Western Ohio is mostly lake plain soils with no rocks, while Eastern Ohio is glacial till with many rocks to slow down installation. Most tile is placed at or just deeper than 30 inches in depth to get the most drainage efficiency. Again, it depends on the terrain, and other factors. Many soils we have, have what is called a fragipan which blocks water flow downward through the soil profile. Tile should not be put much below this layer because it can seal over the tile in a few years. Tile only needs a slope of 1 inch in 100 feet to work properly. Of course the most important item in a tile system is having an outlet to drain the field tile. Without a good outlet for the tile, the tile is worthless. By outlet, I mean exiting the main tile into a ditch, stream or river by gravity to allow the excess water to exit the tile system. A plugged tile system (no outlet) is actually worse than none installed.
If you just have a few wet areas, you can just put tile lines through those to drain them. Just size it right and install it so it can be added onto in the future if you decide to add more tile.
If your fields are fairly flat, say 1 to 2 percent grade, some land levelling or surface drains can help in removing excess surface water to help your legumes grow.
You need someone with some experience in shaping them so they are flat enough and slightly pitched to get rid of the surface water. Surface drains are basically a very wide waterway that really does not affect the farming operation.
I think that is enough detail for now. Hope this helps give you an idea what
may or may not work for you. Ask around at the coffee shop to see who may
have experience with your problem and can help give you some ideas. Good luck.