A good set of headphone is going to be more immersive than a sound bar, but like Barty was saying watching with them all the time may not be great depending on personal preference. I ended up picking up a set for TV/Movie after gaining a roommate (I'm an insomniac) and a neighbor with a newborn (duplex with a shared wall). I honesty didn't think I was going to be 100% on board with them, but turns out I prefer it most of the time. In my particular case i was finding I was hearing more ambient "stuff" in the shows and it really did pull me in a bit more. Specifically with Battlestar Galactica, I kept taking the headphones off thinking someone was at the door, something that never happened with the soundbar.
If you're not blasting the volume, there shouldn't be any issue with hearing damage, and honestly I think I use a lower volume with the headphones than I do with my soundbar. Granted your mileage may vary depending on the headphones you use and the media you watch.
As for models to look at, if you can go with ones that use radio rather than bluetooth. You're going to deal with less latency issues and fussing over codecs used. The downside to RF models is that they're dedicated to TV usage. Bluetooth, while not my preferred, does allow you to use the setup on any device with Bluetooth, so a good set of headphones can serve double duty and can be a bit easier to justify. Now if you do decide to go bluetooth there's a couple things to keep in mind.
1. You will need a transmitter if your sound source (TV, console, computer, etc) does not have one built in.
2. You will need both the transmitter and your headphones to have Low Latency compatibility. Most people start noticing latency issues (audio/video not syncing up) after about 50ms of latency. Your basic bluetooth is typically in the 100s if not worse. So best bet is look for sets specifically listed as having low latency. If it doesn't list it, chances are it doesn't have it, with the exception of the Bose I list below. AptX Low Latency (atX-LL) is what I generally look for in a setup as it's a better audio compression codec and it designed for things like watching TV without latency issues.
Here's the short list I made for a client who was looking to do the same thing.
For RF models:
Sennheiser RS 185 RF - $290
https://www.amazon.com/dp/B00TOT9G1W/?coliid=I6VDHAPG0JKMA&colid=YWFQM6GK4E9T&psc=0&ref_=lv_ov_lig_dp_it
These are the ones I have. Open soundstage, cloth over the hear cups, balance controls and overall a comfortable set. It has a charging cradle and takes optical or analog inputs.
Sennheiser RS 175 RF - $185
https://www.amazon.com/dp/B00SLUI5SA/?coliid=I1K12ZDOKGV2E3&colid=YWFQM6GK4E9T&psc=0&ref_=lv_ov_lig_dp_it
Closed back, so you should get better bass response than the 185s. Leatherette instead of cloth cups, but still around the ear, it also has a charging cradle and takes optical or analog inputs.
For Bluetooth:
Transmitters:
Avantree Priva III aptX Low Latency Bluetooth 4.2 Audio Transmitter - $40
https://www.amazon.com/dp/B01N5KKUR0/?coliid=IKF9A0R82ZJ7K&colid=YWFQM6GK4E9T&psc=0&ref_=lv_ov_lig_dp_it
I have this one and it's pretty good. I used it to hook up to a normal pair of headphones to see if I could deal with wearing headphones without committing hundreds of dollars to the cause. Only real downside is it's 3.5mm input only, so if you're going from an optical in, or RCA in, you'll need adapters.
Avantree Audikast aptX Low Latency Bluetooth 4.2 Audio Transmitter - $50
https://www.amazon.com/dp/B077MXFJGQ/?coliid=I2DIRB8MDGUOUQ&colid=YWFQM6GK4E9T&psc=0&ref_=lv_ov_lig_dp_it
A step up in transmission strength, but the big thing is getting a wider selection of audio inputs and it can act as a pass through for a receiver.
Avantree Oasis Plus aptX HD Long Range Bluetooth Transmitter Receiver - $70
https://www.amazon.com/dp/B07BQYYDNJ/?coliid=I17E83FQD1NNPS&colid=YWFQM6GK4E9T&psc=0&ref_=lv_ov_lig_dp_it
A big step up in transmission strength, but the big push for it would be it can act as a receiving unit. So you could use it to broadcast from your phone to a audio setup. Likely major overkill for watching TV on the couch but it's worth knowing about if you want to go whole hog on a setup.
Recivers/Headphones:
Avantree Clipper Pro aptX Low Latency Bluetooth 4.2 Receiver - $30
https://www.amazon.com/gp/product/B01LZRB8HJ/ref=oh_aui_search_detailpage?ie=UTF8&psc=1
This was the other half I used when deciding if I wanted to deal with headphones while watching TV. With this, you can hook up any setup of corded headphones and have bluetooth functionality. It's not perfect, but if you already have a pair of headphones you like, or the bluetooth models arent doing it for you, it's a good alternative.
Bose QuietComfort 35 (Series II) $300
https://www.amazon.com/dp/B0756CYWWD/?coliid=I32FAXUGF0GDR3&colid=YWFQM6GK4E9T&psc=0&ref_=lv_ov_lig_dp_it
Not cheap thats for sure. But great audio, and I noticed no latency issues when I was testing them. I have big ears and they managed to fit inside the ear cups, so you shouldn't have issues with headphones pressing against your ear. If you have a Bose store nearby they often have these refurbished for a good chunk off the price. If you have a credit card with points or air miles, these are often on the list of stuff you can buy with points/miles.
Plantronics Wireless Noise Cancelling Backbeat - $199
https://www.amazon.com/dp/B01MY4P9EZ/?coliid=ILX3CN05P7D0F&colid=YWFQM6GK4E9T&psc=0&ref_=lv_ov_lig_dp_it
Widely reviewed as a good set of headphones and is low latency.
Avantree Active Noise Cancelling Wireless Headphones $70
https://www.amazon.com/dp/B079N9D8P4/?coliid=I2M4DH1WWC2HVQ&colid=YWFQM6GK4E9T&psc=0&ref_=lv_ov_lig_dp_it
Not widely reviewed but inexpensive and supposed to be decent quality.
Avantree 40 hr Wireless Bluetooth 4.1 Over-the-Ear Foldable Headphones $70
https://www.amazon.com/dp/B01A0EAYDI/?coliid=IVP1TA2P4BZS2&colid=YWFQM6GK4E9T&psc=0&ref_=lv_ov_lig_dp_it
Combos:
These two are bundled with a transmitter. I believe they're the same model headphones as the ones listed right above, just with different transmitters, so likely a better deal then buying them separately.
Avantree HT3189 Wireless Headphones for TV Watching & PC Gaming with Bluetooth Transmitter $80
https://www.amazon.com/dp/B072V3478X/?coliid=I26V16NBAF9951&colid=YWFQM6GK4E9T&psc=0&ref_=lv_ov_lig_dp_it
Avantree HT4189 Wireless Headphones for TV Watching & PC Gaming with Bluetooth Transmitter $90
https://www.amazon.com/dp/B07CJ2BVSP/?coliid=IV8UDT07PB2CI&colid=YWFQM6GK4E9T&psc=0&ref_=lv_ov_lig_dp_it
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