Changing things!

Yes, I would certainly run it past the staff and then exclude any thoughts which suggest comfort zone tendencies.

Definitely consult the staff.
As someone who has just arrived with your fresh eyes, you think you see lots of room for improvement but you need to find out if there are reasons for the way things currently are.

I've worked in places where new management has come in and changed things almost straight away. Often they've had to backtrack because the changes didn't work out.

Take your time to see how things are done now and which of them work well; consider keeping those. Then try introducing new ideas slowly, one at a time, and assess whether they are successful before moving on to the next thing. Your staff will appreciate being consulted, too.

Having been on both sides of the debate, I would say watch first, see what's working, get to know your staff & involve them in the changes.
Have you asked them what they'd like & would your ideas be a step forward?

As another poster suggested it would depend upon your position in the hierarchy and who else is involved in the decisions and the culture of the organization. It might be better to wait until you have got your feet under the table so as not to seem too pushy. Perhaps the three month mark.

Stationary/stationery. My mum taught me 'E for envelope'.

Before you suggest anything and instigate changes - it's stationery. Just to help you to retain credibility. ?

Pen - stationery
Car - stationary

A relaxing room sounds great.

Are you in a Senior Management role ? If so then surely it’s part of your job to suggest things that will benefit the Company.
If you are on the shop floor it might be best to wait awhile and then approach your line Manager with any suggestions.