There is a database for that too: "Linking Animal Models to Human Disease Initiative" http://www.lamhdi.org/ was specifically designed " to make it easier for the biomedical research community to locate, identify, apply and build upon the most useful animal models for their research"
Try also this link, a "site provides information on methods and sources available to reduce, refine or replace animals used in teaching, testing, and research" http://awic.nal.usda.gov/nal_display/index.php?info_center=3&tax_level=1&tax_subject=183
It all depends on what hypothesis you are trying to address in hypertension: 2kidney-1clip; aortic coarctation (between the 2 renal arteries or at the trans-ascendant aorta), 1kidney-1clip, 5/6 nephrectomy (removal of 1 kidney and the remaining is being reduced to 1/3 of its original mass), aldosterone-alt hypertension or Doca-salt hypertension, chronic nitric oxide inhibition, salt-sensitive hypertension (Dahl-SS), spontaneously hypertensive rats, social-stress hypertension in mice, angiotensin II-induced hypertension,...etc. So it all depends on what do you want to address.
Generally rodents such as mice and rats are the starting point. They are the cheapest to purchase and maintain. They are not the equivalent of "small people", but most researchers use them. You would need a pretty large budget to experient with larger species, such as dogs.
I agree with Dr Rhaleb, the model depends on the disease that you want to study and the mechanism that you want to test. Some molecular mechanisms would be better tested in vitro using cardiomyocyte cell cultures. Mice are used to study al, the diseases that you mentioned, they are even used for arrhythmia studies. You just need the right tools and equipment.
Hypertension is a multifactorial disease involving complex interactions between genetic and environmental factors. Development of experimental models of hypertension allowed dissection and isolation of various factors associated with regulation of blood pressure, inheritance of hypertensive traits, and cellular responses to injury. The phenotype-driven approach is taking advantage of selective breeding of animals (primarily rats) that exhibit a desired phenotype, like the useful SHR. Genotype-driven models include transgenic techniques, in which mice are the most successful for selective deletion or overexpression of target genes. Notably, a combination of comparative genomics strategies and phenotypic correlates enhances the utility of hypertension models and their clinical relevance. Indeed, experimental models enabled development of targeted interventions aimed at decreasing not only blood pressure but also target organ injury. Continued utilization of experimental models simulating human hypertension, particularly those that combine other clinically relevant comorbidities like obesity or hypercholesterolemia, may afford development of effective strategies to address this common disease. Nevertheless, a cautious approach is mandatory when experimental findings in these models are extrapolated to human hypertension.