Hi, A property was purchased (house) for approx $15k and it was then sold for approx. $84,000, how would I record this transaction. Would I set the purchase of the house up as an equity account?

No.

Your original entry when you purchased the home (assuming you paid cash):

Dr. Property - House 15k
Cr. Cash* 15k

*If financing was used, this would be a note payable that would be reduced over time as the house was paid off (interest would be recorded monthly as well).

Depreciate Home over useful life:
Depreciation Expense xxx
Accumulated Depreciation xxx

Sale of House entry:

Dr. Cash 84,000
Dr. Accumulated Depreciation XXX
Cr. Property - House 15,000
Cr. Gain on Sale XXX

As you know, land is never depreciated. However, its current value is likely to deviate significantly from its historical acquisition price. Improved real estate, such as office buildings and warehouses, are depreciated, but their current market values may actually increase over time. So if a business owns significant amounts of real property, the historical cost principle can significantly distort the portrayal of its economic condition.

GAAP does not allow the adjustment of fixed assets, such as real estate, to current market values primarily because managers would constantly be tempted to overstate the value of their fixed assets to improve the appearance of their firms' economic condition. In effect, the historical cost principle is applied because accountants believe that distortions of economic condition that involve understatement of asset values are preferable to distortions caused by overstatements.