What Kate said. Also remember this is not a dog you will romp around the fields with, unless you like waiting four hours for your dog to return from checking every signpost in the neighborhood.
When Kate says "commit to going for a walk" - that means, your walk must extend out within dog earshot from your home. That's a circle with a mile radius straight out from your home. You don't have to cover the entire territory taken in by this area, every time, but your walks must take in a good chunk of it on a regular basis.
Also, as I type, there is a 95 pound dog standing on the bed, with her paw on my leg. I'm not hugely put out (well, she just moved it), but it's a lot of dog to consider herself a lap dog. Most LGDs will go well over 100 pounds. Seriously, that's a lot of dog. It's a beautiful thing to share your life with a dog that's really there in such a solid way, but as Kate says, if the dog has plopped down in a doorway or across your lap while you are watching TV, there's some logistical issues to consider.
Pick your breed and your breeder with great caution. Some of the more primitive breeds are less people friendly. Some of the more "refined" - mean further away from their working roots - are aggressive in odd, random ways (over here it's hard to find a family friendly Komondor as they are mostly either badly bred on farms, or show bred).
A companion LGD cannot be trained by force. Period. They have like, no pain/pressure susceptibility at all.
I just spent two sessions on two separate days dematting Lulu's rear end, which I haven't been able to get to in years. Their coats are made to felt rather than mat in an unhealthy way but ridding them of these mats is still tedious and pulls the skin as it does in any dog. Lu stood patiently for over an hour, with no restraint, both times, while I hacked and combed and raked away.
I remember eleven years ago, my first LGD, was a dog I borrowed from someone until I found one of my own. Duke was a Pyr and his coat was just one big mat - real mats with the skin tied up in them.
I took the sheep shears to him, not actually knowing HOW to use the shears yet, and I think I cut more skin than hair off that poor dog. And yet he never flinched when I just sheared right through a bunch of skin. Holy cow, I'd never seen anything like that in my life.
That made quite an impression on me. I also shortly thereafter asked a real groomer the right way to shave a matted dog, a skill that's since made a difference in many a rescue dog's life!
Speaking of coat, care and shedding amounts depend on the type of dog you are considering.
The classic "big white" breeds all shed like crazy. The Pyrs are the worst, of course, and kennel club breeding has made their coats somewhat less correct in that they often mat rather than cording or felting. There's a huge difference. If you miss a felted or corded spot, it will not tend to progress towards the skin, because the coarse guard hair will prevent this.
Felted mats shed out with each coat change (on shedding dogs), with some exceptions. Twice a year I brush out trouble spots that vary with each dog - tail on all of them, back on Tully, flanks on Min, and Lu should have been getting her "pants" combed out but she wouldn't hold still for it outside. I think she has arthritis in her tail area.
A showy, soft, flowing coat will allow a mat to progress towards the skin, gather in more hair, etc, so you have to groom every day on these dogs. Think giant sheltie.
Komondorak are traditionally corded (non shedding). That sounds like it would be easy care but it's actually high maintenance. The advantage of cords is that if you keep them clean, it's less of an allergy problem than shedding hair. Just less. And that's a big if. And again, you want to go for breeders that have stayed with the correct coat, which is less showy (the cords are very rough and uneven). I've seen Komondorak with incorrect coats that were corded and they looked awful - the cords break at the skin and the dog looks like a mangy alien.
Anatolians are smooth coated. There's a lot of shedding involved there too (think German Shepherd or Corgi), but at least there's not a lot of combing. Zoom grooms are useful to get out undercoat and slick them down, just like with GSDs.