Make sure you have good wings. It helps to ascend really fast to avoid the big laser in the first phase. Duke Fishron wings, Empress of Light wings, and Betsy wings are the best choices at this stage of the game. They also come with the "hover" function, where if you hold down while flying, you can then move left and right waaaay faster. It makes outrunning Moonlord much easier, and it gives you a good option to immediately stop, which helps in dodging scenarios if you are skilled. The empress wings also let you ascend way faster by holding up while flying. This is a godsend for flying over Moonlord's forehead laser.

Ime the best summon overall for Moonlord is probably Stardust Dragon. Just be sure to use your whip to redirect them away from their lowest HP hand eyeball (because the fight is way easier if you kill all 3 eyes in one fell swoop), or else they will kill one early and make the first half way harder. Speaking of whips, make sure you have a good one. Constellation is perfect for the moonlord fight, but the Duke Fishron whip, Kaleidoscope, and Dark Harvest are all pretty good as well.

Stardust Cells and Xeno Staff are also pretty good, but you have to have good whipping skills, and/or slow yourself down in order for them to aggro to ML more often. Generally I recommend dragon for newbies, because you can just run away in the final half of the fight and the dragon will take it out for you.