If you don't want steel Aluminium and titanium are your best bets.
For armor there are aluminum-steel alloys and titanium alloys. Making armor lighter is the biggest benefit you can gain. For more minor alloying components nickel improves both strength and corrosion resistance of steel.
If you aren't restricted to just improving the metal parts of the armor carbon fiber can make it even better, especially if layered with metals. Better cloth is also a big advantage, making the padding under armor out of modern synthetics means you can have a gambeson that are lighter, stronger, and more flexible that actually breaths, using impact foams you can even get better padding especially in a helmets. Clear plastic eye protection would be excellent.
For shields aluminum would be the material of choice as shields are heavy and disposable so the lower performance of aluminum is not a problem, of course carbon fiber would be even better. Titanium would also be an excellent choice it is stronger than aluminum and still reduces the weight.
For weapons aluminum is not good, except for reducing weight in things like crossguards and baskets, parts not subjected to repeated stress, it fatigues and fails under repeated loading. Titanium iron alloys are good for many weapons (a titanium hammer would be brutal) but not great for swords it is too soft, however titanium vanadium alloys allows for tempering and can be used to make excellent swords, especially for longer or lighter swords. Even better for a show it makes weapons lighter meaning your "actors" fatigue slower. A titanium-iron core with a steel outside would be an excellent sword composition.
to get away from the metal parts, for polearms (spears, halberds, ect) the possibility of carbon fiber poles would make these weapons far easier to weild, the king of weapons becomes the emperor of weapons.
If your fine with steel it depends on the weapon and armor, for swords and armor you generally want a spring steel or something close. 5160 and 1060 are considered the better steels for these, (best is loaded word and depends a lot about the goal and design of the piece. The steel you want for a rapier is different than the steel you want for a katana) although composite steels are also common in swords. For things like hammers you want a slightly softer steel (XX40-XX45), while the best axes use a combination of a hard steel edge and soft steel body.
But the real benefit of modern techniques is better precision at every stage, composition (both chemical and physical) and heat in particular is far better. Just by using modern consistent production and heat treating you are already exceeding medieval metallurgy.
Study of japanese sword steel microstructure.
Study of damascus steel microstructure
Study of european sword microstructure