If you’re ever taken an interest in powerlifting, you might have seen old videos of powerlifters using a PVC pipe as a homemade foam roller. Don’t do it. You wouldn’t try rolling your body over concrete, and the same logic applies here, unless you’re into medieval torture devices.
That said, you shouldn’t feel nothing at all, and very firm rollers can better at activating deep tissue sometimes. Often, it really depends on the area of the body you want to work, and some models are better for getting into hard-to-reach-spots, such as the thoracic spine. Trial and error, and playing around with various types of rollers, might be a necessary evil if your budget will stretch to it.
Also, bear in mind that there is a difference between ‘cheap’ and ‘soft’ in the foam roller world. Just because it’s soft, that doesn’t mean it’s worse or won’t do a good job. Cheaper foam rollers, on the other hand, tend to lose their shape and sink in the middle. You can still use it, but you might struggle to hit your shoulders, spine and traps if it’s collapsed and malformed.