I have driven and also taken the bus. IMO there is not much to see to stop for on the trip.
If you get a driver it is a full long day. So it is about 7 hours driving plus stops.
I would think that , a driver would be look at a fee from 2500 baht. You could ask the people in the Hotel or guest house, they would have a cousin or a friend who would drive you.
Last time I drove back I stopped for snack and a coffee. The Fist class bus does stop and road side place for about 20 mins
I got this driver in Chiang Rai recommended by a Tripadvisor reviewer, unfortunately I cannot find that posting anymore. The driver's name is Suphakrit, email is email@example.com, he is based in Chiang Rai. He offers to be my driver when I will be in Chiang Rai in December 2018. He emailed me he charges 1000 THB a day. You got to ask him what is included, and like I said, I have no experience with his driving yet.
We used Jermsak to,drive us from Chiang Mai to Chiang Rai. We stopped at Doi Suthep temple on the way out. We visited the White temple on arrival in Chang Rai and the next day spent a great day outdoors with him, hike, elephant ride, river boat ride with a BBQ lunch. Best two days ever. He is an excellent driver and guide. Just a wonderful person. His English is excellent and his price is very fair. His contact email is under the private guide list - in Chiang Rai- on the right side of the page. That is where his home is.