Pick up rental car-- Venice? Padua? somewhere else?

Why not pick up the car in Bologna? If you want to focus on the area between Bologna/Parma and Northern Tuscany that seems like the most logical choice to me.

Yeah- I was wondering if that would be smoother. We didn't know how much there was to see between Venice and Bologna.

If you really absolutely need to pick up the car in Venice, the easiest and most logical point would be at the parking structure on Piazzale Roma. All rental companies are there. The City Parking Garage is the multistory building in the photo below, on the background behind the vaporetti ticket building.
https://images.app.goo.gl/VyVTrBeRP4p1Jw4W9

However if you are staying in Bologna, or in any city, you should reconsider if and when you need the car at all, because Bologna is a congested city with lots of traffic restrictions (only residents’ vehicle allowed in the city center) and awful parking situation. From Venice to Bologna it’s a quick 90 min high speed train ride, downtown to downtown. Also if you intend to visit other cities in Emilia (like, Parma, Modena, etc.) you are also better off visiting those cities by train from Bologna. Having a car in Italian (or European for that matter) cities makes as much sense as having a car in Manhattan, basically an expensive hassle. European cities are much more easily visited using public transportation (trains, buses, taxis)

A rental car is however useful to visit the countryside. You should rent your car only for the portion of your trip that involve visiting the countryside. Tuscany is probably where you will need it. So rent your car in Bologna at the end of your Emilia visit and drive to Tuscany. Actually you could even take the train down to Florence and rent there. The drive from Bologna to Florence is just 50 minutes on a freeway almost totally under some very long tunnels under the Appenines mountains. All you’ll see is the tunnels’ walls.

I would shop around the area to see where you can find the best rental car prices. Cars are often much more expensive in big tourist cities like Venice. Look in Padua and Treviso, and possibly also Verona. All are easy train rides from Venice and 30-60 minutes on a train could make a huge difference in prices.

For rental car prices I always use www.AutoEurope.com. It’s a very reputable consolidator/broker based in Maine which utilizes the main car rental companies in Europe (Avis, Budget, Europcar, Hertz, Dollar). Their deals are often cheaper than going directly with the rental companies.
I also recommend that you select the zero deductible option, as it costs only a few dollars more per day and it will provide peace of mind.
Many people in this forum use AutoEurope.
Regarding selecting a pick up city rather than another you will discover using AutoEurope that prices won’t change at all whether you pick up in a city rather than another. The main driver of price is the dates you select and the number of rental days. July is the priciest.
Once again choose your dates of rental judiciously for the period you really need it. A car is a hassle to have in a city (parking is expensive too) and to visit other cities from Bologna it is best to use the train which will drop you right in the city center of any city. Limit your rental car to the time you will be visiting rural locations and the small villages of Tuscany.

Thank you so much everyone! As a little more context, we are a family of 4 traveling together (2 parents, plus boys ages 11 and 14). Our focus on the Bologna/Parma leg of the trip will be food (obviously). If we decide not to get a car, will be be able to access food production-type places? We assumed we would need our own transport to get to dairies or whatnot. We are pretty flexible-- not eager to have a car more than we need one. Thanks again!

First you need to decide what you want to visit and locate where it is. Also don't expect that they let you enter inside a food production factory at your will. There might be some that allow visits, maybe have exhibits, even tasting, but you need to do some research ahead of time, it's not that you can find these places just driving around by following the smell of cheese. Once you know where you want to go, then you determine the way to get there. If it's within the city, you can probably walk or take public transportation to it. If it's a location out of town center, even if there are no buses, then you can certainly take a taxi to the place from the train station. There might even be organized tours to visit some of the dairy factories in the Parmigiano-Reggiano area. So you need to do some research.
But if all you want is eat, there are plenty of restaurants in the city center of any city in Emilia.

Yes- I am definitely not planning to just stop where I see cows, haha. We will plan the details- I am asking for general advice from those who have been in these areas. Thanks again.

Plan the details, then decide. But as a general rule, there is no place in Italy that cannot be reached by public transport. Factories are often out of the city center or even out of town, but all within an easy drive from the station by taxi. Also research if they have organized tours or excursion where they visit multiple dairy factories. I'm sure they have some in Parma or Reggio Emilia. Start from here:
https://www.parmigianoreggiano.com/

This has all been helpful. Thanks everyone!