Macs by the numbers
McCulloch made dozens of models of the 4.9 cubic inch saws, the 1-51 is but one. All are similar, main differences are muffler type, gas tank capacity, and top cover design. I have several: 1-41,1-43, 1-51, 250, etc.
Most had .404 by .050 chain and hard nose bars. I have converted some to .404 by .063 and a couple to 3/8" by .063 sprocket nose bars.
To determine your chain pitch, measure the center distance over three rivetts, and divide this number by two.
When properly tuned and with a good sharp chain, this saw will pull a 36 inch bar. I use full skip chisel chain on the 36". If you plan on using the saw for real wood cutting, then ditch the hard nose bar and put on a new sprocket nose bar. A 28" bar makes a nice handling unit. And put on a rim and drum, get rid of the spur sprocket!
I would pull the carb apart and check the fuel pump diaphragm. It should be flat with no holes or creases. A common problem with these old macs is a worn out fuel pump diaphragm. You can find carb kits at some saw shops that have been around for a while, or on Ebay. Most have a tillotson HL carb.
Another common problem is loose plug in connections on the wiring from the points to the coil, and a loose spark plug wire connector where it plugs onto the spark plug. Put in a new J6J spark plug.
Any or all three of the above (bad carb fuel pump diaphragm, loose wiring, loose plug wire connector) will make the saw hard to start and it will run bad. I would pull the flywheel and put in new points and condensor.
If everything is right, the saw should start on 2 pulls with fresh gas.