Silver hite,
Thanks for the questions.
To my knowledge, all the beta-blockers have the potential to block conversion of T4 to T3, but I have never seen this to be a practical concern. This effect of beta-blockers is used to advantage in patients with thyroid storm, but otherwise the effect is not noted by patients or clinicians. In fact, many patients who think that something is interfering with their thyroid medications have simply been the recipient of a varying dosage throid medication. Synthroid, in particular, is notorious for having varying concentrations.
Furosemide is not a very effective diuretic. Most clinicans use hydrochlorothiazide (HCTZ) or a combination of HCTZ with triamterene to avoid the potassium loss.
To call beta-blockers "heart medications" is a misnomer. Beta-blockers do not exert effects that are particular to the heart. They work by blocking the effects of adrenaline (and its congeners) on vascular receptors, some of which are located in the heart. They are considered one of the safest anti-hypertensive medication classes when used appropriately.
Asking which hypertension medication is best for someone with hyperthyroidism is like asking which car is best for an old person. Other factors are more important. Talk to your doctor to help guide your decision. I would think that the first line agents in most people would be diuretics or ACE-inhibitors, followed by beta-blockers.
Hope that helps.