The "no or slow engagement" into gear is often referred to as "morning sickness" in the transmission world. This is caused by hard or broken rubber sealing rings on the clutch apply pistons. Heat and age are the root cause.
The only fix is to rebuild the transmission with all new internal seals (yes, I have known people who don't replace those seal rings).
You can probably baby the transmission along for a while (I babied mine for two years until I got time to rebuild it) as you save for or plan the time to rebuild. If you have a daily driver the I would recommend getting a core and rebuild it and then spend a day swapping the transmissions.
After you get it rebuilt be sure to install a cooler in front of the radiator to lengthen the life of your new transmission.