I started using the original Silvretta touring binding which were heavy but reliable and worked fine. The Dynafit Tech bindings came along and I couldn’t resist the weight saving. They also proved to be reliable and place the hinge nearer the toe so they feel more like X-C kit. I had some (non)release issues but once I set the forward release lighter than my normal piste settings they were fine (this involved changing the spring at the time but is now the small screw).
I tried an original Fritschi but the movement felt odd because the hinge was so far from the toe, they also suffered breakages at the time so I opted for Tech.
There are lots of brands in the market now and recently I saw someone out on some Fritschi/Marker type bindings on which they’ve added a link in the front hinge to improve the motion. I’ve tried to find them with Google and failed.
Boots are a personal thing. When choosing bear in mind that the looser and more flexible the top part the faster you’ll go up. Look for boots that allow a maximum of amplitude without too much heel lift that don’t press on your toes when moving the ski forward with the boot open. Downhill I’m happy in any old flexible boot but you might not like minimalist race boots if you like carving on piste or jumping off things. I generally strip the boots of spoiler and superfluous velcro straps, and add elastics to buckles to stop them flapping when completely undone. Madame thermoforms her inners, I prefer not to.