I like to remember Alpha properties by envisioning a blood vessel end-on. To me, it looks a lot like the big loop in the Greek symbol for Alpha. This is a good thing, because the Alpha properties of vasopressors primarily serve to constrict peripheral vessels, thereby "shunting" blood to the core organs, heart and brain (although they also tend to constrict micro-circulation there as well) and thereby increasing blood pressure.
The Greek symbol Beta looks a heck of a lot like a stylized heart turned sideways, and the Beta properties of pressors generally work there as well, increasing heart rate (chronotropy) and force of contraction (inotropy).
Pressors can work primarily in one way or the other, or both. Epinephrine has about equivalent properties for both Alpha and Beta. Dopamine is interesting, because at low doses it has primarily Beta properties, whereas at higher doses, the Alpha predominates. Another drug that we used to use in the ACLS algorithms, Isoproterenol, is basically all Beta.