If you do weight training (bodyweight or with weights) or cross training, choose a model with a solid base to stabilise your bodyweight. The width of the sole, especially at the forefoot, is important to encourage proper toe movement and ensure good balance throughout your movements.
During a fitness session, you are performing a variety of movements at different paces. The theoretical impact in most disciplines is low, but the need for cushioning varies from one person to another (based on build, injuries, shoe habits). If you have a greater need for cushioning, you should check whether the shoe has a shock absorption mechanism, as well as the type, hardness and thickness of the component used for the sole.
If you do fitness regularly, support is a very important criteria to consider to keep your feet healthy in all disciplines. It can, for example, be characterised by side reinforcements and an effective lacing system that adapts to the shape of your foot.