Gutting existing propane fireplace/TV to build alcove?

Looking at maybe moving. House has a propane fireplace which I am definitely removing. Picture attached. Two questions:

1. Would it be easier to make an alcove out of the existing TV/fireplace area or just gut the whole thing and do away with the alcove idea? Seems like if I keep to the alcove idea I don't have to worry about the finish work on the side shelves and ceiling. Also would like to have a TV to the right of the alcove so it should provide some better protection against heat from the stove.

2. Once I get the propane lines safely unhooked and remove the existing fireplace where do I start?

This will be a first for me, gutting a part of a house. I can hang siding/windows/trim/doors/basic plumbing but being all self-taught looking for a little guidance here in terms of gutting this area while keeping the rest of the area as clean as possible. I guess I have to remove tiles/drywall/cut any wood that is framed between these two walls (i.e whatever holds the TV in place). Any tips/pointers/heads up would be appreciated. I have already been reading about how to build the alcove itself - just looking for tips on gutting/prepping this area for an install.

Thanks!

Definitely getting rid of the TV. Would gut it pretty much all the way to the ceiling and put the TV to the right. I just wonder if keeping the alcove would be easier to keep it looking clean as I am no professional carpenter. I.e. no worries about having to change/finish the benches and/or finish the ceiling if the entire thing were to be removed.

Looking at coastal Carolina; similar climate. Hard to keep it burning all the time 24/7 because the weather gets into the 50s so much here in the winter but when I'm home the heat pump goes off and the wood stove takes care of it no problem in my current house. Hoping to do the same if we move. I can work out dimensions of the alcove etc later, just a little nervous gutting something like this for the first time.

Thanks for the reply