Are you selling the place or living there? Bathrooms tend to be small so it's better to buy expencive 50-60 usd range paints that have anti microbial properties. One gallon of expencive paint and a gallon of primer so you don't waste your paint should do great. I will copy paste some stuff I found on a paint website. I reccomend asking for help when you buy bathroom paint the person behind the counter should know what you want to buy.
Flat: Nice matte coating, but best in low-traffic areas where it is never or rarely touched; absorbs moisture, so it is bad for bathrooms; great for halls and dining rooms
Eggshell: Slightly "******" and more washable and scrub-able than flat; best for places without a lot of moisture
Satin: Has a bit of a gloss, somewhat more than eggshell, and can be used in low-moisture bathrooms
Semi-gloss: Excellent finish for any kind of bathroom; repels moisture well and is not ultra-shiny like high-gloss
High-gloss: Toughest option for bathroom walls but looks awful over large surfaces such as walls; best for smaller surfaces like trim and cabinets
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