That is a very long list!
The best thing to do is look at the list as guidance and see what you already have.
For example baby bath, surely you already have a kitchen sink, bathroom sink and a shower or large bath. Use those. We put a towel folded at the bottom of kitchen sink and bathed in there a lot, or just bathed baby in main bath with us.
Things like baby towels?? Just use erm a normal towel I'm sure you have loads of
Etc etc, there's many things in your house you already have a similar thing for, and it's better to use as most things you will only use 6-12 months, 2 years maximum.
If possible just get a cot or cot bed instead of crib. They will last newborn- regular bed age, so no need to buy crib and then cot after 6 months. For downstairs I would just use your pram laid flat/ carrycot prt if you have/ or just a blanket folded up on the floor. Remember few babies can move before 6 months so if you lay them on a sheepskin rug/ blanket on the floor when small they aren't going to be escaping around the room ( and would just roll onto floor safely if they did roll)
Extras like a baby bouncer/ jumper/ rocker I suggest don't buy at first. Wait and see what your baby is like. If they are happy to be laid on blanket on floor or on you then just stick with that, as most bouncers you can't use once they can sit up anyway as can pull chair over so again you only get a few months out of things.
Much better to save the space stuff uses up for later on when they have toys, and save the money to actually do something with baby/ child like swimming