I’ve got a mio alpha which I absolutely love. Of recommend without any hesitation. None of the faff involved with chest straps. Works with blue tooth and ant+ so it’s very flexible, as well as having a live display of BPM. The rechargeable battery has a good life too.
Whatever you get make sure it uses coded transmission, otherwise in a gym you’ll be picking up all the other people’s sensors too. Bluetooth and Ant+ are always coded, cheaper models (for example the bottom end of Decathlon’s range) may not be.
My recommendation would be a Polar FT1 – it’ll be coded, and almost certainly compatible with the cardio machines at the gym.