Lots of good points on grease above, but consider this. Some grease is designed to "bleed". they work well in sealed bearings. Some are not, they work well in pin joints. Grease is a combination of an oil (wich can have a thick or thin viscosity) and a "soap" base. The base is normally lithium, most common, or calcium for higher temps. Sometime other additives are added like graphite or moly. For sealed bearings a #1 consistancy grease should be used. For not well sealed bearings a #2 with a heavier base oil should be used. For pin joints a #2 or 3 with a heavy base oil and possibly graphite or moly.
OK, so now how do I get by with one grease ? If you are running heavy equipment a lot, you don't. Use the right grease for the right part. For me running a JD on a part time basis and some other small equipment, I use a #2 grease recommended for auto chasis lube. (today these greases provide excellent lubrication in lots of applications). If you use this for pin joints, grease often.
Even a good grease gun will bleed some greases through the nozel, especially in warm weather. The most important consideration is how much pressure can the gun produce to free up and clean up tough joints. A lever gun is better than a pistol grip and should put out 3-5,000 psi. (You can check with a grease fitting attached to a pressure gage.)