If you wish to ride her bitless, then there is nothing wrong with that. For now, you can just stick with the halter and lead if she is responsive enough in that. Though in my honest opinion, there are much better options out there rather than a mechanical hackamore. When I want to go bitless on my horses, I either use a soft hackamore (a rope halter with mecate reins) or a bosal hackamore. Again though, if she responds well in the mechanical hack and doesn't seem to have any issues with it, then it will work fine to keep her in that. She probably would need tack designed for a large horse, the best way to know what size bridle she would need is to get one of those soft measuring tapes and measure over her poll to each corner of her mouth, across her forehead where the browband would lay, and then behind her ears and around her throatlatch. You should be able to take those measurements to the tack store and find a bridle that will fit her. Some tack stores will allow you to bring the horse to them and try saddles on them until you find one that fits. However, if that isn't an option for you, given her size and breed, she would probably need a saddle with Full Quarter Horse Bars (those are about the biggest you can easily find without going to draft sized tack) and the gullet would probably need to measure 7 1/2 inches.
Here is a good site that will teach you all about western saddles, their parts, and how to size them. Saddle Gullet - Gullet Sizes
Wow, sorry for the novel.