Q: My car jerks when putting it into drive and sometimes has to be revved up high before going into gear

I'm sure the problem is my transmission I'm just not sure if it could be a simple fix between a linkage or solenoid. I start the car and put it in Drive and it jerks into gear about twice before it will go, as for other times it will rev up high and finally go into gear. The car does have high mileage which is what makes me believe it's the transmission. The fluid is clean and full still after 5k miles and does not leak. I've made sure always to use Honda atf as it can be picky with other fluid. I recently changed a tensioner pulley as well as 2 motor mounts and 2 transmission mounts due to hearing clicking when accelerating. Also no check engine light is on nor has it come on.

My car has 205000 miles.
My car has an automatic transmission.