Note: As my answer is very long, I have a concluding paragraph at the end.
I’m going to assume this Naga is more snake than human, meaning they have snake’s head and lower body with an human-like upper body. I will assume they are about 18 foot long with 6 foot standing upright and weigh about 1000 lbs
I feel they would be like Roman Legionaries. They did not wear much leg protection due to their style of combat. Instead of trying to armour the lower body, only the upper third or so of the Naga’s body would be armoured (the upper third as snakes can move just as fast with 2/3rds of their body on the ground as they can with 3/3rds and im assuming Naga can too). So then Naga would wear armour similar to what we’ve seen on humans in history on their upper half with their lower half completely bear.
Whilst it may seem like a huge weakness to have 2/3rds if their body exposed, their style of combat can accommodate for that. Below is a video detailing how Naga might fight in combat: https://m.youtube.com/watch?v=2uVRKKdIYLI
Naga would use large rectangular shields that protect their body, reducing the need to armour their lower half. In a battle field, they would be in a large shield wall so it would be almost impossible to get around their shield to attack their exposed lower body. In a duel, the Naga has a lot of manoeuvrability so can keep the shield in front if their opponent. They could also coil their lower body up, reducing the amount of area they’d have to protect.
I would suggest some kind of metal armour (full plate, brigandine, coat of plates, lamellar) but it depends on the look you want to portray.
Snakes often loom (stand their upper body straight up off the ground) and expand their hood, if they have one, in an attempt to look bigger and more intimidating. I would incorporate this idea by having large shoulders (like Italian full steel plate armour). You could do what rich Ancient Greeks did, having muscles built into the armour. There could be a chain mail coif with additional pieces on either side to mimic a snake’s hood or the frills you mentioned (note though that, unlike many images you find on google, historical mail coifs had padding underneath them)
In regards to helmets and armour, something to note is female Naga would not have breasts, these are mammalian features. A female Naga would be flat chested so ‘boob plate’ armour (fantasy steel plate armour with defined breasts) would not develop in their society (not that it would be necessary, there is already space between armour and the body. Boob plate is similar to a Muscle Cuirass. It is slightly less effective if it dips in the middle of the chest but not significantly so).
In my world, sexual dimorphism is shown in the heads and body shape. Female Naga bodies are usually smaller and narrower than the male’s and have less broad shoulders. This is similar to male and female humans so I won’t go into this much further. Instead, the more interesting feature is in the heads. My male Naga have oval-shaped heads like this: 0 where as females have more triangular heads like this: /\ I based these shapes on the differences between venomous and non-venomous snake heads and art work I saw. This means that Nagas may have helmets that are shaped significantly differently depending on the gender of the wearer. This is just something that you may want to consider for aesthetics, both in and out of armour. Having different shaped heads makes it easy to instantly tell apart males and females without giving them “feminine” features found in humans, such as breasts and long hair.
To conclude, Naga would likely have armoured upper bodies with completely exposed lower bodies but have a large shield to compensate. Their armour would probably be metal based (full plate, coat of plates, brigandine, lamalar, etc) with large shoulders and a mail coif that looks like a cobra’s hood. The physical shape of the armour would be made to fit with an individual Naga’s body shape with females typically being smaller and more slender and with female helmets being more triangular and male helmets being more ovular. I hope this answers any questions you have and any questions that you might not of thought about.