Going with solar be sure that you end up with a digital charge meter in the system whether it is an integrated one like with some of the Blue Sky charge converters or something like the Trimetric. It is the only way to know accurately the charging and discharging status and true battery charge level at any point in time.
We use solar as a zero maintenance option to using a generator to recharge our batteries after a night of camper use. That does not provide enough charge to run a microwave at 1000 Watts or a hot plate but it does provide enough for the fridge electronics, furnace blower motor, water pump, lights, and LED TV operation. We use the microwave and hot plate when we are at a campground with hookups where we can use the 110v AC. The rest of the time we use the propane cooktop and this is hardly a hardship in any way shape or form.
Check your TV's power draw. Most LED TV's I have looked at that are 19" and smaller draw at most 40 Watts at 12v or less than 4 amps. With 3 hours of use that is a total draw of less than 12 amps which does not put a big dent in our total capacity of 110 Ah (50% of the two 110 Ah 12v batteries). Having the old tungsten lamps in use in the camper can draw as much from the batteries as the TV will and so changing them to LED lamps is a good first step.
Our 200 Watts or 12 amps of solar charging brings the camper's batteries back to 100% before noon regardless of the season or latitude where we are camping.
I do not understand the fetish of having to have a microwave. I never had one at home until I was in my 30's and while it is convenient at times to heat a cup of water for tea or to reheat something from the fridge it is far from being a necessity. In the camper we use it when shore power is available for microwave popcorn and to cook vegetables and that is it. When shore power is not available we make do without the popcorn and cook the vegetables as a stir fry.
If I was going on a long expedition the microwave would be the first thing I would jetson (along with the hair dryer and electric percolator and rice cooker) and use the space for storage of things I would actually need.