All good points. First thing to do however, is to pull codes from the OBDII port, any decent auto store should be able to do so for free. Could certainly be misfires from worn out spark plugs, but could be faulty injectors also, besides the transmission possibilities. So, codes first.
Check to see if transmission fluid level is correct. Low OR high can cause problems. Is the fluid color good, and free of metal shavings? Any leaks on the ground or on the underneath of the engine/transmission?
Can you feel the vibration/shudder in PARK when revving the engine, or only when driving? Could be wheel/tire, loose lug nut(s) or alignment also.