You are right in thinking that a simple fluid and filter
change will help the hard shifts. When I had
problems with my transmission, I experienced
"slipping" -- when I would accelerate, the
transmission would not "catch" and I would
have to manually put it into 1st gear in order
to get it to engage.
I would have the fluid and filter changed first.
It's not too expensive -- around $130. The tech
that does it will drop the transmission pan, and
that's usually where clutch material collects,
signaling a major transmission. From the
sounds of it though, you probably just need
a filter and fluid change.
Best of luck to you and have a good week!