10% sounds about right. In practice you wont be able to apply the Steinerhart-Hart eqn because Beta will change a bit (or a lot) with temperature. Getting accuracy over 100C range will be hard work. Note the often quoted "B25/85-value 2880 to 4570 K" Values. This gets added to your basic tolerance. Your DAS is 12-bits but you'll likely only get 7-bits from a thermistor set up. Run the opamp on 3V3 or less and lose the zener. If you have a long lead, put a small cap across the thermistor to contol RFI. A higher precision opamp wont hurt but given the low starting accuracy you might be wasting your money. A semiconductor sensor might work out to be economical.
Actually, the Steinhart & Hart model was originally designed to account for the change in effective beta with temperature, and it will comfortably model the resistance/temperature behaviour to better than ±0.5˚C over a 100˚C range - provided its parameters are optimised for the individual thermistor. Even better results can be had if you include the missing second-order term. Thermistors are generally quite stable over time, but they are difficult to make repeatably to close tolerances. Most of the quoted error comes from unit-to-unit variability, unless you pay a lot for close-tolerance matched parts.
Assume the resistance of your thermistor at 0˚C is 5kΩ and that at 100˚C it is 500Ω (these values are about right, I think). Then with a 2.75k reference resistor the ADC reading will be 2642 at 0˚C and 630 at 100˚C. So you get a total range of 2012 counts - 11 bits resolution near as damn it. This should plenty for your needs, even though it is not evenly distributed over the temperature range.
To get the best calibration results, you should have about twice as many measurement points as you have calibration parameters & make a least-squares fit, so ideally 6 different temperatures. 0˚C is easily realised using an ice point: with care, you can get within 10mK quite repeatably. For the other 5, the best way is to use a stirred water bath (e.g. a saucepan or
bain marie) with a reference thermometer (but keep your thermistor leads dry, unless it is a fully waterproof type). This is OK up to about 90˚C. Alternatively, use an aluminium 'dry block' with holes drilled for the thermistor and reference thermometer. This can be heated in a domestic oven (not a microwave!), ideally a fan type, with a thermostatic control. If you use a reasonably large block the temperature within should be uniform enough for your needs
For the accuracy you need (I'm assuming ±1˚C), the typical K-type thermocouple thermometer is not accurate enough. A good T-type thermocouple should just about be OK, or a known calibrated thermistor or better, platinum resistance thermometer. A precision semiconductor sensor is also OK, but not all of them maintain their rated accuracy above 85˚C.
A good rule of thumb is that achieving anything better than a genuine ±0.5˚C calibration uncertainty, except over a limited temperature range such as for a clinical thermometer, is difficult and will cost you serious money.
I second the recommendation to put a small capacitor across the thermistor leads, at the ADC input. It keeps EMI out and maintains a low impedance at high frequencies, required by the ADC's sampling input.
Have fun!
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