I’d caution against getting a unit hot enough to heat more than your bedroom. Think of how hot your room will be every night when you want to go to bed.
I have a gas fireplace in my bedroom and master bath. Both are 16,500 BTU’s with a blower. My master bedroom is about the same size as yours at 350 sq ft, and my bathroom is about 175 sq ft. The house was built in 1999 and is well insulated.
Some things I can say about my experience is the standing pilot alone is about enough to heat the room. I’m always reminded when its on because when I walk in the bedroom it’s warmer, and I’ve yet to turn on the pilot in the bathroom. Your room sounds cooler from the start, but I’d see if you can get one with a intermittent pilot.
Also, I have one of those Bed and Breakfast style DV fireplaces that’s taller than it is wide, and mounts about chest high in a cabinet. Beautiful thing about that is on those cold snowy nights I can set the timer or room temp on the remote, lye in bed and watch the flames as the flakes come down. With a traditional fireplace you will only see the light flicker and it will likely take up more room.
Lastly I would stay away from a free-standing gas stove. I’d think the temptation to leave a piece of clothing on it would be too high which could cause a fire.