wood stove/insert for 300sq ft

Why close off all the other rooms? A small insert like my 1.6cf Lopi would not run you out of the house. I heat just under 1200sf with mine in the same climate. It's not heating me out of the living area and takes some time to get enough heat out for the whole house.

I would go with a stove that has the capability of heating 1200 sq ft. It would be nearly impossible to just heat one room, the benefit of the stove is the ability to heat a whole floor, I live in a raised ranch, I have my main level floor - Kitchen, living room, dinning room, (3) bedrooms in a rectangle configuration, the basement area is approx. 35ft x 25ft then garage space under the bedrooms. I installed the stove in the basement (BK princess) and I'm able to heat the whole house from it. The whole point is to maximize your heating area.

Welcome!

As others have said, heating only 300 sqft with a wood stove will be difficult. An EPA-approved secondary burn stove will need to reach a certain temperature in order to burn clean and efficient. At that point most stoves will deliver more heat than what you will need for 300 sqft. You could look for a very small stove; Morso has several models with a firebox ~1 cu ft but those will require constant refueling and may still overheat your living room. May I ask what is the reason for closing off the rest of the house?

For a low and relatively constant heat output a small catalytic stove would be best. What are the inner dimensions of your fireplace and the depth of your hearth? One that could fit your requirements would be the Woodstock Keystone: http://www.woodstove.com/keystone It has a height of 28" so you could maybe partially recess it in your fireplace as long as you can still access the side door. Due to its catalytic operation you can burn it at lower temperatures which will give you long burn times without heating you out if the house. It will still probably prove too much for just one room. Some non-catalytic small inserts that may somewhat work for you: Pacific Energy Vista/T4 or Neo 1.6, Regency I1200 or Alterra CI1200, Osburn 1100. For a budget option you could look at the Englander 13NCI (although it is a bit larger than the other mentioned) or a Century CW2500.

What you will need in addition is a full liner to the top of the chimney which should be insulated for safety and better draft. The rest of the chimney should be closed off with a block-off plate: https://www.hearth.com/talk/wiki/make-a-damper-sealing-block-off-plate/ You will also need dry wood with an internal moisture of less than 20% for your stove. It is very rare that you can buy that so most members split and stack their own. Depending on the species and drying conditions that needs to be done up to three years in advance before you can actually burn it. If you don't anticipate burning much you can also look into compressed wood logs like Envi-blocks, Bio-Bricks, Northern Idaho Energy logs etc. They will be more expensive but much less work, guaranteed dry, bug free etc.

Many chimney sweeps will also do a stove install. You can look here for a certified one: http://www.csia.org/search
A block-off plate is rarely included. Most only stuff some (fiberglass) insulation in the damper area. However, that does not provide an airseal and is an inferior solution.

Don't expect to heat the basement from the first floor. Warm air will rise, not go down the stairs. However, 800 sqft sounds like a more feasible area to heat without overdoing it.

Installation prices can vary greatly between different areas and each install is a bit different but to give you a ballpark: I would anticipate about $1600 to $2000 for liner and install.