We sit about 12' from a 85" flat panel TV in our family room. Upgraded from a 64" TV. The first question my wife asked "Is that really bigger than our old TV?" - It's just a TV, even a big TV, and it will still feel like a TV.
Standard screen size is about 10" to 12" of diagonal for each foot of viewing distance. 120" is definitely the smallest I would go, and I would go as large as 150" diagonal if you like it.
How do you know if you like it? You buy a projector first, then the screen second. Have the electrician come in after you have determined the screen size and projector location to put the wiring in place. Most electricians know very VERY little about how to do A/V properly, so you may want to look for a good path to run wires yourself and keep in mind that HDMI didn't exist 16 or so years ago, and the newest 4K HDMI didn't exist until a few years ago. What you have today will be obsolete in a decade. You want to be able to put new wiring in place as easily as possible.
You may want to look at projectors which support long throw distances like the Epson 5040UB or the JVC RS440 (I'm a big JVC fan). These models support 4K resolution and can be had for under $3,000. Most of all, they can be put at the BACK of your room and project all the way across it. This may minimize the wiring that is necessary. I actually did a setup where I just ran the cabling from the ceiling to the floor and had some equipment right there.
Another rather large consideration is that you will need to address audio completely separately from video. Projectors don't have much audio built in. Better models have no audio built in. They should be treated like computer monitors. Don't count on good audio or smart functions. Just a display device. That's okay because you can get a Roku for not much cash and you want good speakers to fill your space with good audio. But, once again, A/V receivers have to support the newest HDMI (2.0/18Gbs). They aren't terribly expensive anymore and you can get packages for under $500 with speakers. (Spend more if you can)
Yes, a projector is not a hang and bang project the way a TV is. It's tougher to setup. But, once it is in place, it's truly as good as going to a movie theater. It has the immersion that a movie theater offers and it has the feel of being special that a theater offers. I can't tell you how stoked my kids and their friends were when I told them they could play the Playstation on our front projection setup in the basement. They went straight to it and enjoy the heck out of it.
Front projection really can start right at about $1,000 for a complete setup, but a good JVC is about $3,000 and good audio can be way, way more than that. So, it's a range starting at $1,000 for a very entry level 1080p setup. I think the price jump that may occur for having to go from the center of the room for a standard zoom range projector to the extended zoom range of the JVC or Epson model may pay for itself for the ease of getting cabling in place.