I never did puree foods. BLW is baby lead weaning. So foods cut appropriately is where I started. I let baby take the lead. Also, rice cereal has zero nutritional value and most likely contains arsenic. I would definitely avoid that. If you choose to feed, i would offer oatmeal.
The right approach is whatever works for you and your baby. Fully baby LED weaning with no purees, puree only or a mix of both are all totally fine options as long as your baby is getting what they need. I have done a mix of both approaches and that worked best for us. So when you're pediatrician says it's okay to offer rice cereal, that means he or she thinks rice cereal is a safe and healthy option for your baby at this point. That doesn't mean it is the only option. I personally chose to use whole grain baby cereals over rice cereals, but I give my baby the rice mum mum biscuits. I think every baby is a little different too, I know a lot of people's babies took to solid foods right away, my daughter had some additional issues with choking and swallowing her entire life and needed a more gradual transition for safety, but I added in textures and solid foods as early as possible because I don't want her to have an aversion to textures. Do what is best and safest for your baby.
i did a few purées and she hated them so i started doing like bananas and fruit (in the fruit pop things) and then gave her puffs and stuff and now she eats whatever just not meat really