I use beta/biothane exclusively for my bridles, and am starting to switch over for my halters as well. There are many good online retailers for these types of bridles, which come in everything from an english style with cavesson and flash nosebands to simple western versions, halter-bridle combos, and sidepull/lateral (Dr. Cook style) bitless versions. I would start at www.endurance.net and look through the tack stores that advertise there; most carry some form of beta/biothane tack.
Personally, there are Amish nearby that make beta biothane bridles much more cheaply than these online retailers, so I tend to use those. I use both an english w/cavesson for my direct reining horses (in snaffles or pelham with double reins) and a western version for my neck reining horse in a mild Myler curb. I look for good quality stainless steel hardware and prefer “normal” colors like black and brown, so that the tack has the look of leather, without the hassle.
Another thing to consider is that I prefer the textured look and feel of the beta vs the slicker biothane. They’re the same substance, just different texture from what I know. (not an expert). It’s also a lot easier to handle beta reins when wet than normal biothane, which will slither right out of your hands unless you’ve got iron fists of doom. Most retailers let you choose which you want your tack made from.