You need to measure the diameter of the crankshaft extension, where the clutch is attached to it. It will be either 3/4" or 5/8". If it is 5/8", either a Briggs and Stratton or a Honda of 3 to 4 hp will bolt straight on, subject to not getting one with a different shaft length from the original. If it is 3/4", you would need to buy a replacement clutch-half of the 5/8" size for around $85. Other than that point, the replacement is a simple bolt-on fit.
Whether you choose a Briggs or Honda is a question of what you want to pay, and what access you have to good second-hand engines in your area. At one extreme, an old 1970s or 80s Briggs Model 80202 should cost very little, and was the engine that replaced the Kirby-Lauson as original equipment on that mower during the 1970s. At the opposite extreme, a new Honda GX120 is the nicest engine, but rather expensive. There are many intermediate solutions between these extremes.
