The safest choice for protecting computer equipment and the best when it comes to noise-sensitive operations like audio recording is going to be one that generates a pure sine wave. The abrupt changes in voltage that can occur with simulated (stairstepped) sine wave response is not good for power supplies or the NUCs themselves. In this day and age, the additional cost of a UPS with pure sine wave generation is fairly minimal, so do it right.
The next part of the decision is the capacity you require. This is dependent upon two things, what you want connected to the UPS (and available during power outages) and the length of power outage that you want to be handled. The typical 100mmX100mm NUC is going to be in the 65W to 120W range. The larger form factor versions can go much higher. Determining the requirements for other equipment is easily handled by following the guides provided by the UPS manufacturers. The larger manufacturers - CyberPower, APC, etc. - all provide online guides for determining what you require. Some even provide calculators that take care of this for you.
Hope this helps,
...S
