Never felt the need for an belt doing any workout. Even for PR training. I have worn one in the distance past when going for a max of 1 or 2 reps.
To wear it correctly you will have to have someone help you tighten it to the extreme. If you can get one finger in between the belt and body it's not tight enough. Inhale strongly as you cinch the belt up. You going to restrict the breathing quite a bit, that's why 1 or 2 rep only. If you feel that there is not enough support for the small of the back, than fold up a large towel and put it at the point of the small of the back. That is one of the main reason why a custom fitted lifting belt should be first choice, if into serious lifting, that is.
In strengthening the core (over worked term I know), pay attention to exercises like GoodMornings, SLDL', Romanian DL's, hypers, etc.. First choice, for me, would be GM'ings in a PR. Also train the ab wall heavy and hard. The upper/lower ab pack is a very powerful short range muscle group. If total core training is desires, than some direct oblique work. Though DB and general overhead pressing can affect them also.
Not wearing a lifting belt does not always mean that the mid section/core will be well trained. Added insurance, with belt or no belt, would be some focused lower back and ab work. The whole trunk (interior/exterior) area will benefit, giving a strong base for power. Good Luck.