Technical Question - What can this problem be? Diagnosis?

I own a 1997 4Runner with the 3.4L 5VZ-FE V6. I have 304,000 miles on it. I have had the timing belt replaced (2 years ago), plugs and wires replaced recently with tune up (8 months ago). I use 91 octane fuel and the vehicle is well maintained.

The last 2,000 miles I have noticed a mild rough sounding clatter when the truck is first started and the engine is cold. Outside temp is average 50-70 degrees F. It sounds like the valves are running roughly. When the engine warms up it seems to go away. The rough sound and slight power loss remind me of using low octane fuels but, I am using 91. Also, recently, the same rough sound is briefly apparent when shutting the engine off (but not as predictably with start up).

Also for the past 10,000 miles, during engine start up, there is (about 30% of the time) a single pop noise that comes out of the engine compartment. It is not particularly loud but definetly noticable. It sounds like a small engine backfire.

Does anyone have any ideas about how to approach this?
Thank you!