Hey Paul,
You need to have a tire and wheel balanced because of the high spot in a wheel and tire. Every wheel and tire has a high spot. If the high spots are not countered with weights, you will get a horrible vibration in almost every case. There are machines that are able to do a "match mount" we call it. Where we put it on the machine, then it tells us where to rotate the tire on the wheel to get the best balance. I have seen a wheel and tire that didn't need balancing, maybe once a month. But I have never seen an entire set. And usually a new set of wheels you have the best chance, but since your wheels are used, you will need it. You can ask to have the match mount, but they will charge more, but it is usually worth it! Hope this helps!