I live in the Midwest and my 1995 Country now has 330,000+ miles and I have always gone with the standard 10w30 and 5w30. The main consideration is what climate you live in - then check what is the recommended weight for the temperatures you are driving in.
Above 0*F 10w30 is good. Below that 5w30 should be used.
Jeep recommends 10w30 for above 0*F and 5w30 for below 0*F (I believe I have the temps right) I have had good luck using 5w40 synthetic oil in my 4.0L.
10w-30, the recommended type should be on your oil filler cap, located on your engine, right side, valve cover.
5w30 or 10w30
10W-30
5w30
The 2002 Jeep Grand-Cherokee has overhead valves (OHV).
The 2001 Jeep Grand-Cherokee has overhead valves (OHV).
The 2007 Jeep Grand-Cherokee has single overhead cam (SOHC).
A 2005 Jeep Grand Cherokee uses DOT 3 fluid.
A regular Cherokee uses Dextron A Grand Cherokee uses Mopar ATF+4
The trans is called a 42Re
The 2003 Jeep Grand-Cherokee has overhead valves (OHV).
The 2004 Jeep Grand-Cherokee has overhead valves (OHV).
The 2002 Jeep Grand-Cherokee has overhead valves (OHV).
The 2001 Jeep Grand-Cherokee has overhead valves (OHV).
The 2010 Jeep Grand-Cherokee has single overhead cam (SOHC).
The 2013 Jeep Grand-Cherokee has double overhead cam (DOHC).
The 2009 Jeep Grand-Cherokee has single overhead cam (SOHC).
The 2005 Jeep Grand-Cherokee has single overhead cam (SOHC).
The 2014 Jeep Grand-Cherokee has double overhead cam (DOHC).
The 2011 Jeep Grand-Cherokee has double overhead cam (DOHC).
The 2006 Jeep Grand-Cherokee has single overhead cam (SOHC).