I make several different kinds, twisted, straight and braided. My recommendation is to NOT try to skip out on your core. Braid it with the same intensity you would braid anything and you'll be happier with the results. I always roll and hang or stretch all my cores, I have a really old stove iron that I tie the braid to, then hang it from the ceiling for a few days. Works like a charm!
When I twist one, I tack one end down, twist it, then stretch it as tight as I can get it, then tack the other end down and let it dry for a couple days. I haven't had any untwist... yet. (keeping my fingers crossed!)
I also build some smaller bosals with a couple straight strands for a core, just be sure to tuck them back through with the tails of your other strands when you build your heal knot, and only use for 3/8ths or smaller bosals.
When I braid one, I use anywhere from 4 to 12 strands, and I try to make it as smooth and tight of a braid as possible. I drilled several different sized holes in a hard board and I grease my braid up really well, then pull it through several times, and smaller and smaller holes to even it out. Sometimes after braiding and hanging them, I sand them down a bit to be sure they are the same diameter for the whole length. As was said earlier, the smoother the core, the smoother the braid.
I've also used other cores that can work well if your looking for something special, like an old 1/4 or 3/8 mecate, yacht braided nylon cord, leather rounds, braided leather and multiple cores. I really like the multiple cores for larger hackamores. Use a 6 strand core, then braid a 12 strand over it, then 18 for your final braid. It takes a lot of rawhide and time, but they make really nice hackamores.
Your best bet though, as mentioned, is obtaining broken reins/reatas or buying cheap reatas off ebay. They work great for cores!
Hope this helps a bit!
On your braided cores, it also helps to bevel all four corners.