How do doctors determine what high blood pressure medicine to presxcribe to you?

Choosing the right high blood pressure medication can be tricky.
Dozens of high blood pressure medications are available, each with pros and cons. Depending on how high your blood pressure is, your doctor may prescribe one or more high blood pressure medications to treat your condition.
Your doctor may first suggest diuretics. Diuretics work by flushing excess water and sodium from the body, thus lowering blood pressure, which may be enough along with lifestyle changes to control your blood pressure.
A diuretic may be the only high blood pressure medication you need. But under some circumstances, your doctor may also recommend another medication or may add another medication.
Those choices include:
Angiotensin-converting enzyme (ACE) inhibitors eg. captopril (Capoten), lisinopril (Prinivil, Zestril) and ramipril (Altace).
Angiotensin II receptor blockers eg. losartan (Cozaar), olmesartan (Benicar) and valsartan (Diovan).
Beta blockers eg. metoprolol (Lopressor, Toprol XL), nadolol (Corgard) and penbutolol (Levatol).
Calcium channel blockers eg. amlodipine (Norvasc), diltiazem (Cardizem, Dilacor XR) and nifedipine (Adalat, Procardia).
Renin inhibitors eg. aliskiren (Tekturna)

How you respond to your medication will determine what medicines you stay on. Often it is trial and error and can take several months before the best treatment is found for you.
For more information see: https://www.drugs.com/condition/hypertension.html

It all depends on how high your blood pressure is and how quickly the doctor feels you need to get the blood pressure down to a safer level.