Transmission slow to engage

I have a 93' cutlass ciera automatic, 3.3 w/158k miles. I have change the tranny fluid, filter and seal, also the oil and filter. The car start great, even goes into reverse quickly with no thump, bump, knocking or rocking. BUT (note I have no tachometer) from a stand still I have to bring the rpm up pretty high before the transmission engages. I have to hold that for about 4 or 5 second before it begins to move. Aside from that everything else work good breaks, speedometer, starter, alternator even the neutral switch sensor. Twice I was told I need a new transmission and neither time was a diagnostic test done. The car has a small shake as it goes into gear 1 out of 5 take offs. The inner gears shift as they should after the car gets moving, even the lower gears shift when I change from the column while moving. It just that take off from any gear. Drive, 2nd or 1st.