These are the bathtime essentials that you need. I've narrowed down the options based on the preferences you shared with me and highly rated products.
Skip Hop Baby Bath Tub ($33): This option is great if you want a sling seat for extra flexibility. The sling seat in this tub can adjust into three positions to grow with your little one. The main downside parents reference is the bulkiness, but if you have space this could be a great option.
Angelcare Baby Bath Support ($19.79): I'd recommend this option if you already have a tub or sink to bathe your little one in. This seat provides the extra support you need when bathing your newborn. It's net design also makes it easy to rinse soapy water off and it's made from mildew resistant material.
Stokke Flexi Bath Tub with Infant Insert ($64): I'd recommend this bathtub if you want a simple basin that folds flat. Parents love this tub because it has a deep basin and can be used with bigger toddlers. The plug is also a heat indicator to make sure the water temperature is just right for your little one.
Cetaphil Baby Wash & Shampoo with Organic Calendula ($7.99): A gentler option.
Puracy Natural Baby Shampoo & Body Wash ($12.99): A plant and mineral based option developed by doctors.