If you have a favorite nylon halter already, you can easily purchase nylon or bio/beta-thane “clips” to attach your bit to the halter rings (up by the horse’s eyes). For reins, use any set you have and buckle them to snaps. The snap can clip onto the bit or the halters lead ring.
horseDOTcom has Weaver Halters with nice hardware for $15. They also carry snaps that you can attach to your reins to make them easy to move from the bit to the halter.
http://www.hought.com/end-bh.html has “bit hangers” in biothane, if you look at endurance sites you may find nylon or other prices, but this seems like an average price.
The problem I had when using a basic halter and clipping the bit to the eye rings is that often the halter’s poll strap would slip down the back of the neck and change where the bit was held - a simple homemade nylon brow band fixed that easily (I recycled a nylon dog leash). (It probably doesn’t bother most horses but it did mine.) But I found that I much preferred an “add on” headstall - it fits over my rope halter and snaps to it so I don’t need a throatlach plus it already has a browband, and the bit doesn’t shift around in my horse’s mouth. (here’s an example - https://www.thedistancedepot.com/Deluxe_Add_on_Headstall_p/bbt-dah.htm)
Hope this provides some ideas!