Welcome to Columbia! It's a pretty great town.
For family practice, I highly recommend Namaste Healthcare in Ashland. I was sent their way by others on this forum last year and we've been really happy with them. They are extremely supportive of breastfeeding and are ok with delaying/spacing out vax. And they have a very sweet office cat!
For farm eggs and produce, we've got a pretty awesome farmer's market that just this year has extended through the winter months. The Root Cellar is a great resource too, and offers a CSA-type subscription service. Oh, and the local Hyvee's make a point to stock local eggs, meat, and occasional veggies.
Our wee one is just a year, so I don't have any recs for good ped dentists or homeschooling, sorry!
I've lived in Columbia for the past 11 years with a 1 1/2y stay in Hawaii after college. This is a great small town with the diversity of a city b/c of the university (and Columbia College and Stephens to a small degree I'm sure). Lots of great parks and the MKT Trail system is a blessing!
When we found out we were pregnant last year we were also told to go to Namaste but of the three times I've called them since last July, they have told me everytime to call back later b/c they weren't accepting any new clients. So, we still haven't found a family practice we really like even though I've heard there are some good ones in the University Physicians close to the intersection of Green Meadows and Providence. I own a kids art studio in town (Creative Days) and used to be a preschool teacher so I hear alot about different schooling options here. We host a homeschool class on Tuesday during the school year and two of our kids don't belong to any community and the other one sometimes does stuff with a co-op group of which I can't think of the name of right now.
As far as eggs, we get ours from the Stanton Brothers who sell them at the farmers market in the ARC Parking lot on Ash Street (they also deliver to Clovers and Hy-Vee).
Welcome to our town and I hope you're settling in!