You're on the right track with using the equity accounts as you are.

A QuickBooks company file should always represent a single "business entity"...in this case, the farm business.

When you pay a farm expense with a nonfarm account (maybe a personal credit card) you are making a capital addition to the farm business (increase in equity). Same is true if you have W-2 income or other nonfarm income that you deposit in the farm checking account. And if you pay a personal expense with a farm check, you are making a withdrawal of capital (decrease in your equity invested in the farm business).

I prefer this approach to using Other Income and Other Expense, but if your farm operation is a sole proprietorship (not a partnership, LLC, or corporation) it doesn't matter much, and that approach will work too. Standard use of Other Income and Other Expense accounts are for recording income or expense which is attributed to the business but outside the realm of normal business activity--like maybe a big casualty loss.

Volume I of The QuickBooks Farm Accounting Cookbook™ (a book I wrote) has a section on nonfarm income and expenses, including using equity accounts for that, and how to track different income and spending categories as subaccounts.