You can get and keep a second class medical with well-controlled hypertension. It is one of the easier medical conditions to get certified with, and if all blocks are checked the AME *may* issue your medical certificate at the time of your visit.
Almost all standard BP meds are approved. MAO Inhibitors are not (they are rarely used these days). A big part of the evaluation is to look for end - organ damage (renal insufficiency, cardiac disease, etc)
Concur with AOPA - their medical assistance services are excellent and are by themselves worth the cost of membership.
Remember when you go to your AME to have with you exactly what is called for on the FAA Hypertension exam protocol (available to members on AOPA.org) and nothing more. Too much information can screw things up, as will not enough.
In general it's a good idea for your personal physician to NOT be your AME. Your personal physician owes a duty to you. The AME owes a duty to the FAA. In some instances, could be a conflict.