For a horse that neck reins well, you can ride in either a snaffle or a curb of some sort. You can find shanked bits that either have a dogbone or french link mouth on them, but I am not a fan of shanked bits with broken and/or floating mouths like that. I much prefer something solid that my horses can pick up and carry instead of just packing around.
Any one of these should suit your needs well. I use bits either exactly like these or very similar on all my horses and, while certain horses do have their preferances between them, I've never had one that didn't go well in at least one of them (though they often went well in all but liked one better than the rest).
And, while I don't have one of these, I like the way they look and plan to try one soon.
As for nosebands, it depends on what kind you're talking about as there are several different things that are all called "nosebands" in the western world.
There are tie-downs, which are nosebands attached to the front cinch via a strip of leather/nylon. Those are designed for horses to brace against them in high torque events like roping and barrels so that a horse can maintain balance and strength in a sharp turn or a hard stop.
Then, there are bosalitas, which are often used with a "get-down" rope. I can't seem to find a good picture of one on a horse but they look like this. The rope is tied around the horse's neck at the throatlatch then run through the rawhide noseband. They are traditionally used on ranch and/or vaquero horses for leading/tying instead of using the bridle reins.
Then, there are cavesons. Basically, they are a noseband designed to try to keep the horse quiet on the bit...though I think they are more of a crutch than anything in that regard. IMHO, there are much better and much more effective ways to get a quiet horse, but that's beside the point. They are just strips of leather/rope/rawhide with or without decoration that are not designed to withstand any sort of pressure from leading/tying/tie-down/etc. They are used almost exclusively with snaffle bits.