You can find the model number by Googling "vintage Singer sewing machine", then click on "images". Match this sewing machine to a photo to learn more about it.
Is this a "portable" Singer in the dome case? They are not terribly popular because of the weight (always support the case from below when carrying it, as the machine can actually fall out of the dome case). Where I live, you might get $50 for one that is in pristine working condition as you describe; most would sell for around $30. A cabinet machine would be priced differently, as beautiful cabinets are worth more. Be aware that my pricing is for the usual vintage Singer machine. There are some vintage models that are worth a lot more because they are rare. This is why you really need to know the model number of the machine; the years it is made does not provide enough info.