I have a few things to say on the topic. Hope it helps!
First off, please, please, please be careful actually flushing "flushable" liners. So many times they cause problems down the road. My suggestion...buy them, use them but don't flush them. Just throw them out. Often times things that deem themselves flushable like that or cloth diaper safe (referring to creams and all) really aren't. You won't notice a problem for a while and then one day, boom, you have repelling issues or you are calling a plumber. Just my advice. The cost and hassle of that just isn't worth the chance to me.
I think that how many diapers you need depends on what kind you decide to use. I absolutely love my best bottoms. They are an All-in-2 system. It's one size with several rows of snaps (I don't like any Velcro diapers) to adjust the fit around the waist and legs. The shells are the costly item in this system but because they are reusable unless you had a messy poo, you don't need as many as All-in-1 diapers. The inserts are great too. Those come in 3 sizes but a lot of people only ever use 2 out of the 3 sizes during the diapering years. That just depends on the baby for which size people skip, if any. I love that I can add absorbency by using what they call a doubler or overnight insert, or just stacking a second regular insert on top. I just love how cute and adjustable they are. It's the only kind I'll ever need.
Keep in mind when you make your decision how you plan on laundering your diapers. If you don't want to use the dryer, you will want to buy more so that they have time to hang dry. And an all-in-2 system will take much less time to dry than an all-in-1. I like to hang dry mine and then fluff them up in the dryer for a couple minutes when done. Toss the inserts in the dryer with some wool dryer balls...then I've got nice, clean, dry and soft diapers.
With my first baby, we did not use cloth diapers right away. For one, we were trying to focus on adjusting to parenthood, but two, we had soooo many disposables gifted to us that we decided to use them. It made life easier for a bit and I honestly found it a relief. Baby's first poos are very messy and sticky. There's no way I would have wanted to deal with getting that off my cloth diapers. Yes, best bottoms will fit a newborn.
Oh, and one last thing...diaper sprayers are awesome (we hooked up a bidet sprayer to our toilet). Even for exclusively breastfed babies. Spray the poo off first and save yourself some trouble with staining. Stains will still happen from time to time but I think it helps if it isn't sitting on there until laundry day. The sun is awesome for treating stains btw (even on a cloudy day).
This may be way more than you asked for, sorry. I could go on forever. I am passionate about cloth diapering and the system I use. No matter what you end up choosing or kind you use, know cloth diapering was the best decision I ever made for many, many reasons.