The main thing that identifies a strain is it's "terpene" profile. These terpenes give a strain its smell and contribute at least 50% of the overall theraputic effects. This makes the terpene profile pretty important when choosing a strain (it should be listed on the product, otherwise ask the budtender). Since you're looking for anxiety management you'll want terpenes that have anti-depressant and calming/relaxing effects. You will want to avoid strains with high levels of stimulating terpenes (eg terpinolene, ocimene and pinene).
The first 4 terpenes in this image are good anti-anxiety options:
If you're using essential oils that contain these terpenes then there are no issues of dependency or rebound anxiety. It's cannabinoids that contribute to these effects but only when using high THC products without other balancing cannabinoids (eg CBD) and relaxing terpenes.
As for cannabinoids: the most common one is THC but you might find CB
D or CB
G more suitable since they tend to be more calming/relaxing. You can buy CB
D or CB
G products but there's also products that include some THC + higher CBD, eg 10% THC, 20% CBD. The CBD helps to smooth out the THC effects. The key thing to remember is that higher THC is not necessarily better for anxiety. Also, go for strains with a high overall terpene content will offer better medicinal value.