All my chickens are unvaccinated. I keep a closed flock (no new birds arriving) and have never seen signs of disease other than fowl pox (carried by mosquitoes).
So that only leaves coccidiosis (which is a big problem with chicks). However you can raise chickens without medication if you make sure they have exposure to small amounts of coccidia from a young age, and don't let the bug get out of control. Feeding soured milk seems to be a really good cocci preventive in my backyard.
The brooder must be clean but not sterile. I always throw a handful of adult healthy hen soil into the brooder from day one. This gives the chicks exposure from the day they hatch, and stops it overwhelming them when suddenly exposed to it later on. I also move chicks out of the baby brooder at exactly 3 weeks of age (which is when they begin to shed high numbers of cocci oocysts) so the brooder isn't seeded with huge numbers that could overwhelm new chicks.
There's a bit of an art to it (watching weather, changing litter every 24 hours at the first sign of chicks going off feed) but raising chicks without medication is perfectly possible. For a first timer I'd probably suggest either raising these chicks under a broody hen or using medicated starter.
Sorry to suggest medication but if the birds have a good couple of months between having any medication and going clean they should be pretty well free of residues.
I raise several batches of chicks per year, but raising fairly low numbers is the other key to avoiding cocci. Problems happen when too many chicks are raised on the same ground.
Hope this all helps, sorry it's long winded!
With you in spirit,
Erica