When I first start the car, I can get the transmission to go from neutral/park to reverse without much trouble.. I may have to wait a second or two for it to get into gear, but I don't have to rev the engine to do it... But when I try to go from reverse/park/neutral to drive, it always takes a few seconds of revving the engine to get it to drop into gear.
Doesn't matter if the car is warmed up or not first, and even setting the gear shifter to 1, 2, or 3 instead of Drive still needs the revving in order for it to drop into gear.. though I've found 1 takes less of this abuse to get it in gear. When I am accelerating hard, like when I'm getting onto a highway, the engine will go up to 5k to 6k rpms before shifting, unless I let off the gas for a brief moment above 4.5k rpms. I've also had the transmission drop out of gear entirely while sitting at stop lights and then take several seconds to get it moving again once the light changes.
What could be causing these problems, and what is the best way for me to go about fixing them myself?