Jon, if the engine has performed this way since you acquired the 1986 300E a year ago then it is a longterm problem. There should be no need to warm up the engine for several minutes before driving. The acceleration hesitation could be linked to a faulty Oxygen sensor.

If you're not an avid DIY'er you might consider taking your car to a reputable independent tech trained to work on MB automobiles. Otherwise follow Ben's advice to pinpoint the basic problem. Check the service records for replacement of the distributor cap, distributor rotor, spark plugs and ignition wires. They are all candidates for replacement if they haven't been changed within the last 30,000 miles. Once you get this underperforming engine sorted out you will feel like you're driving a different automobile.

__________________
Fred Hoelzle