Synthroid (along with Lexoxyl and
generics), which contains only T4.
Armour (and other desiccated porcine
thyroid products) contain both T3 and T4. Some people need that extra T3, some don't. It's partly a matter of personal preference and partly what works best for you, preference aside.
You've already had TSH test at 800, so that is a very firm indicator of hypothyroidism. Your symptoms are also classic hypo symptoms.
Be sure to ask your doctor for FREE T3 and FREE T4.