My biggest suggestion for you would be to do a trial run. Our first couple times we had some leaks around the legs or at the hips, mostly from the insert not being positioned correctly. Also the flushie is a bit tricky to get the hang of.
You might want to invest in some cut pieces of fleece to use over the flushie to make poopy ones easier. There's really no way to rip that thing open without touching poop (the pee ones are no big deal).
We go through one cover a day on AVERAGE. (for example, we had a poopsplosion this morning that got on a cover, so we used 2 today, but the second cover is still clean so we can use that again tomorrow). The liners are a breeze to rinse out and hang dry, so you don't need a ton of those. With 4 covers I would suggest planning for a 2 cover rotation, so you have 2 washing and 2 in use.
ETA We haven't used the flushies past the first pack (hated the extra step) and found that we love using the covers with prefolds, so that may be an option for you to keep using your covers.