What are the dates for your trip? How many nights will you have in Croatia? It is never a mistake to develop an itinerary that makes sense geographically and allows you enough time to see the places you choose to visit.
I think the following basic route would work, and I don't see anywhere you would need a private driver or a tour. However, there might be an attractive one-day tour from Split that would get you to multiple interesting places hard to combine via public transportation.
Fly into Split.
See Split, with possible day-trips to Sibenik (train? or bus), Zadar (bus), or Brac (ferry).
Bus to Plitvice in the afternoon. Possibly see part of the park late that day
Plitvice. Finish with park. (You'll probably want a total of 4 - 6 hours there.) Bus to Zagreb.
I haven't been to Sibenik (recommended by another poster here) or Brac. I quite liked Zadar. The medieval center is on a peninsula; it's a bit of a walk from the bus station. Zadar is popular with European tourists, but I still enjoyed several hours walking around after arriving late and spending the night there. Zadar has two worthwhile contemporary monuments on the waterfront, one of which (Monument to the Sun) needs to be seen after dark, which might not work out on a day trip.
Don't try to travel to Plitvice, arrive in the morning or right after lunch, and see the park then. It will be nightmarishly crowded with day-trippers. It's a great, great destination; see it at its best by avoiding the mid-day mob-scene. This is not the place you want to visit on a day-trip!
I like Zagreb a lot. It has a large, bi-level historic district, an active café culture, a bunch of good, traditional museums, and two excellent unusual ones: The Museum of Naïve Art and the Museum of Broken Relationships.
Croatian buses are comfortable. You can Google for schedules, but where buses are concerned, I like to double-check once my feet are on the ground in the departure city. If I arrive by bus, I check the outbound schedule before leaving the bus station. Pay attention to days of the week, and be sure you know of any holidays falling within the period of your visit.
Don't be surprised if you're asked to pay the equivalent of about $1 US to place each suitcase in the hold beneath the bus. I think Croatia is one of the countries where I encountered that.