Hi Derek! Welcome to Permies!
Congratulations on your new house. An exciting time.
A well draws on subsurface
water that is collected from a fairly wide area. The main thing to be careful about is contamination with pathogens. This means ensuring surface runoff (especially in flood zones) cannot top the well head or enter a cracked casing. Manure-intensive activities like
cattle or hog pens that leach too much unprocessed poo are also a potential problem, especially with a shallow well. In my area, there is also a mandatory setback from the wellhead to sewer pumpouts or leach fields. Again, this is to reduce the risk of cross-contamination.
But can you garden the area around it? Absolutely. It's better if the area is sloped so any runoff drains away from the wellhead.
Some pictures inside the well house would be helpful. We can probably tell you a great deal about your well.