There are several classes of antihypertensive drugs, which can be combined with each other, that the doctor may choose for an individual patient, in order to optimize their blood pressure values with the lowest risk of inducing any side effects.
Beta-blockers drugs act directly on the heart, and slow down the heart rate, they are mainly recommended for people with cardiac arrhythmias, and contraindicated for people with a slow basic heart rate; they can cause coughing or breathing difficulties in patients with asthma or COPD.
Diuretics reduce blood pressure by removing fluid via the urine; they are mainly indicated in people with a tendency to retain fluids, but can be associated with a loss of salts (with associated symptoms like cramps and asthenia), particularly if used at high doses.
Calcium antagonists usually act directly on the arteries as vasodilators, can aggravate an underlying gastro-oesophageal reflux and some of them (but not all!) could help with the appearance of leg swelling during hotter periods of the year.
Drugs named ACE-inhibitors or Sartans, are drugs that act on both the vessels and the kidneys. They are usually safe and well-tolerated, but ACE inhibitors are sometimes associated with the onset of a dry cough. They should not be taken with potassium supplements, because these tend to retain it themselves. ACE inhibitors and Sartans should be avoided by women at risk of pregnancy, because of possible adverse effects on the foetus.
In special cases, your doctor may also choose to use different drugs, like peripheral alpha blockers, central alpha-agonists and potassium-sparing drugs.