When I spent two weeks as a summer student at Cambridge many years back, I took the free walking tours with Footprint tours.(Tip based). So if you can't afford a private tour, these tours are just as good.
https://footprints-tours.com/cambridge/tours/cambridge-walking-tours/free-cambridge-walking-tour/
Note, that entry to Kings College Chapel is not included with many tours. You need to queue up at the college and pay separately for entrance.
As for Punting, just go down to the river Cam at Bridge Street. The main punting company is Scudamore, but there are other smaller punting companies. They will have a shared punting ride with guide and punter. Price should be around £20- £22 per person, but advanced booking is usually cheaper than just showing up as I did.
https://www.scudamores.com
Way back then, when the price was cheaper, I just showed up after class and wanted a ride. It was well known to all the students that the going price was £15. Scudamore's tours were filled for the day. So I went to another company offering punt rides and they quoted me £20 and I said "Scudamore is only charging £15." The tout said "OK, £15 it is" took my money and pointed me to the boat a few yards up the river. So if you feel the price has been raised on you. Haggle.
The punting tour was fun and the punter tells "dubious" stories about college life. And on the free walking tour, they also tell the same stories of college life which differ than the punting guide. Interestingly, the stories about the car on the top of college building varied big time, so be wary as to the authenticity of the their stories.
Have fun. Also, FWIW, they sell "Cambridge" labeled sweatshirts and T-shirts to the tourists. Real students get T-shirts and sweatshirts with the names of their college, not a generic "Cambridge" logo.