Either of the canals you mention would be an excellent choice. The LLangollen has enough locks to be interesting (a good chance to chat to other boaters) but not too many to become tiresome. The Mon&Brec has (I think) no locks. The LLangollen is the most popular canal in the country, and I would not advise going there in high season (July/August). The Mon&Brec is isolated from the main network of canals, and is much quieter. Both are very beautiful indeed. If you want a VERY quiet trip, you can hire electric boats on the Mon&Brec.
Locks are not difficult to work if you are fit enough to walk (each lock requires a certain amount of walking back and forth from one end to the other). On a canal with many locks, you would get quute tired, but neither of these canals are likely to exhaust you. It will all be explained at the hire base, where they will show you how to drive the boat (one lever for backwards/forwards, and a tiller - like a sailboat - to steer with). Thousands of people take their first narrowboat trip each year - you won't be the only beginners, and canal folk are very friendly and will help you out whenever you need it.
If, on consideration, you are daunted by the thought of driving a boat and working the locks yourself, google "hotel narrowboat england" and look at a trip where someone else does all the hard work and you just sit back and relax !
Almost all narrowboat trips are round trip - you have to get the boat back to the base you hired from. So you either have to do a "ring", or and "out-and-back". The problem with rings is that you commit yourself to too great a distance and spend the second part of the trip racing along to get back in time, with no time to stop at pubs or explore villages, or have long leisurely lunches on the sunny back deck. With an out-and-back trip, you just turn round halfway through the week or fortnight.
Tips
1) You steer a narrowboat standing up at the back exposed to the elements, so be prepared for a fair bit of standing and a fair bit of rain !
2) Don't overplan. If your trip would be spoiled by not getting to everywhere on the map, go by car instead. Narrowboats travel very slowly (that's the point - it is a relaxing holiday, not a white knuckle ride). Be prepared to turn back without getting to your planned destination when you are half way through your week. Just enjoy the pubs, the villages and the scenery you glide through, without being too fixated on getting to a particular place. You will average LESS than three miles (or three locks) an hour - so three miles and three locks will take more than two hours. Count on averaging no more than twenty locks plus miles per day. Expect to do more, and you will be anxious and frustrated and looking at your watch all the time.
3) Don't overpack. Narrowboats don't have a lot of storage. You won't need many clothes - very few canalside places are posh. Dress for comfort, not for looks. And you can wash clothes on the boat and dry them in the fresh air ! Don't take hard suitcases, there will be nowhere to put them and you will be falling over them, and moving them around, all week. Take soft bags than can be squashed into a drawer.
4) Don't skimp on your boat - the boat IS your vacation. Make sure there are enough fixed beds for all of you. Turning the dining table into a bed at night, and turning it back in the morning soon becomes VERY annoying. An look at the arrangement of bedrooms and bathrooms to make sure you all have sufficient privacy (especially if someone needs to go to the bathroom, or to the kitchen, in the night). But otherwise don't get a boat that is too big. The bigger the boat, the longer it will take you to learn how to thread it neatly through brigdes and into locks. On these narrow canals, you only have about six inches on either side of the boat as you go through a bridge (but everyone makes loud banging noises in the first couple of days, and the boats are made of steel !).
Do read some trip reports on the Web. Google "Narrowboat trip England" (or Wales) and see what other Americans thought of their trip.
If you like green countryside, and English (and Welsh) pubs, and like meeting people, and are willing to try something new, and aren't in a hurry, and don't require guaranteed sunshine - go for it. But beware, you will not want to hand your boat back after a week.....
Yorkshire is not just a pudding