Answer: Cactus need full sun and an exceptionally well drained soil or they will not survive. If you have heavy clay soil, you will have to create a special raised bed for them. Many also prefer a neutral soil pH. To check that, run some basic soil tests and then if necessary add lime to raise the pH.
Here is overview information to help you get started in creating a planting bed for your cactus.
In terms of which cactus to grow, unfortunately not that many are going to be winter hardy for you (your zip code places you in zone 6B). You might experiment with a selection of the Opuntia cactus and consider also growing Yucca and perhaps some assorted sedums to add some variety.
One other consideration is that cactus are sharp, and it can be difficult to weed between them. Many weed seeds can blow in and germinate in gravel beds. Be sure to keep up with your weeding regularly to avoid eventually having a serious weed problem. Good luck with your project!
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