Advice request for small design studio LAN setup (multiple rooms)

Hi guys, first time posting here! I was hoping you wouldn't mind advising me on the best way to go from an unreliable Wi-Fi to LAN setup, with the constraints listed below.

I run a small design studio which is part of an old refurbished factory (old walls, not really future-proofed). Our studio has five rooms; four of these feed off the main entrance reception. In one corner of the overall unit is our broadband router/phone line.

We initially got by on the Wifi from that router, but it wasn't strong enough to reach the other end of the unit (about 30ft?). We're on business fibre with Plusnet (UK).

Temporary solution was to use a couple of PowerLAN units which are also wifi boosters, but long story short, it's not good enough for the wifi, and we're not getting the most out of our fibre even via cable (they are tri-port TP-Link 500mbps models). Our cables are almost all old as well. If I remember correctly, they need to be at least Cat5A for gigabit LAN, and some of these cables are from 2001...

I want to invest in a decent LAN solution. At our busiest, we will have up to 8-10 computers plus about as many mobile devices on top of that. Naturally, my plan is to hook everyone up via cable, and leave the wifi to the mobile devices or guests.

We will also be looking to install CCTV soon (4 cameras), but not sure if it's worth doing PoE instead of BNC (BNC currently makes more sense for this scale). I gather I just need to hook up the DVR to the router or switch, but the cameras have options and PoE is one of them, but it means a bigger switch(?).

So, I started looking into 24 port switches with PoE, long term needs and expandability in mind. Thought might as well aim for something I can put in a rack unit. Now thinking it might be a bit overkill, and don't really want a ton of cables going around the place or creating too much work for ourselves.

Would a 5 port switch suffice in the room with the most computers, and just one cable running from the router in the corner to the other end? Maybe another 5 port for the main room with similarly another cable running between that and the router? My room is in the middle, so should I run a main switch from here? Have my own single cable running around? I honestly don't know what the most sensible solution is.

I'd appreciate any advice, and will try my best to answer any questions! Thanks