pick your field before you start the maneuvers just in case
That's good advice for most types of flying in single engined aircraft!
it would be very easy to pull too hard and over stress something.
Expect that it will be much more easy to over speed than over stress to the point of a safety of flight issue, for modern GA aircraft. The design tolerance for overspeed is only 10% (though you can go that 10% with no damage at all, if you're very gentle in smooth air). Where the design tolerance for over stress is 50%. You really don't want to be in either of those corners, but most spin approved aircraft are in the utility category, which allows 4.4G. That means that it will be 6.6G before you acutally make an unflyable aiircraft. Between 4.4G and 6.6G you will probably bend something expensive and scary. Most "regular" pilots would be shrieking in horror before they applied 4.4G. I have only once, and it was deliberate in a 150 Aerobat. It takes more pull than you think!
That all being said, there is no excuse for an instructor to get anywhere near those corners in a spin approved aircraft. The aircraft is designed with a margin of speed to account for a speed build up after upset. Any spin approved aircraft I have ever spun has lots of speed capacity to allow for some speed build up in the dive recovery, without creating a risk. If you're in the top half of the yellow speed range after a spin (in an approved aircraft), you've done it wrong!
a few people who say it stops almost every time they spin
Respectfully, these people either need more spin training, or should be presenting that aircraft to a mechanic before the next flight!