Kaeya will be your first Cryo user in Genshin Impact, so you will want to get to grips with a good build for him as you may be relying on him for Cryo damage for quite a while.
With Kaeya, you want to take advantage of his fast attacks and rapid movement to position well and hit as many enemies as possible with his Frostgnaw ability, this will allow you a solid uptime for his Glacial Waltz, doing large area-of-effect Cryo damage.
You have a couple of options with Kaeya for good weapons. The first is the Sacrificial Sword. This 4 Star weapon can be obtained from Wishes, and will give a 40 to 80% chance of an elemental skill ending its own cooldown. This allows a lot of Frostgnaw spam, but can only occur once every 30 to 14 seconds, weapon level depending.
Cool Steel will give a damage buff against nemies affected by Hydro or Cryo, which is fantasic if you are doing regular swaps with Barbara. It is a 3 Star Sword you can get from chests, so is easily found, and refined.
You can go with the Noblesse Oblige set, gaining a large boost to Elemental Burst damage, and all party members ATK stats. You can farm the Noblesse Oblige set at the Clear Pool and Mountain Cavern, and you can get the Gladiator Set from Elite Bosses and Weekly Bosses.
You can also mix in the Icebreaker set, which you can get from the Abysal Domains, for further bonuses against enemies afflicted with Cryo or the Frozen status.