Get yourself a decent router capable of running OpenWRT, which will allow you to set up vlan's for your lab, and (I would also recommend) another separate vlan for your IoT and other "smart" devices.

The TP-Link Archer C7 is old but reliable and has a lot of open source support.

If you're feeling more adventurous You could also build your own router with any computer that's got two or more Ethernet ports using PFSense, Firewall-NG, or IPFire

EdgeRouter is proprietary but minimal. You can also look at Opnsense running on a used thin client off ebay.

You can physically isolate by running multiple independent switches, you could run different subnets on the same switches or you could VLAN separate but that would require a managed switch or setting up your topology that something tags the traffic with the proper vid before running on the unmanaged switches. All have their pros and cons but i would strongly recommend getting a managed switch (managed firewalls/routers/switches depending on features/port count can all fill that need) and doing VLAN separation if you don’t have a lot of equipment you’re starting out with.

One of my first projects would be to setup a small Linux box that I can ssh into remotely.

Why not just take the next step and setup tailscale? That way you can learn and also not have to worry about setting up a full security stack and everything for your DMZ.
Tailscale will let you create a virtual local network so that you don't have to expose anything to the internet.

It depends on what u wanna run, I use an old AMD A8-7600B, wich by today standards is less than a laptop cpu. But I run OpenMediaVault wich is just a NAS, so usually my cpu usage with 2 users at the same time is around %40-%60. I recommend u to use passmark as a reference, just tipe the cpu u have in mind + passmark and make thr comparison with mine so u can have an idea.

Manually set up the local IP of ur machine in the router/modem, then in the computer (so everything is failsafe), then configure the firewall (I recommended ufw) and only allow the ports that u need in the necessary protocol, nothing more. Also, to be script kiddos safe I recommend to change the ports of everything that u can, in this case SSH, I don't remember the usual port, but change it to something like 666, 999, 6666, u get the idea, if we aren't the same as every other server in existence we r gonna be safe most of the time, disable password login and use an rsa key.

Managed switch to create vlans and a firewall to manage the traffic.

Past that it's really a case of how much you want exacting control. Even a single /24 network gives 253 hosts and the class C space allows for a whole pile of those, so in theory it'd be easy to put everyone in their own network, but a pain to maintain.

I did this myself for all of 150 dollars. I bought an OptiPlex 7050 off of Amazon and added a dual intel network card. From there, I installed OPNsense. I have a DMZ, WAN, and LAN interface.

You can't both bridge your current router and use it for WiFi AP because of the hierarchy of the network. You'll need either a compatible AP-capable WiFi radio in your be router (hard to find, limited compatibility, I think you might top out at WiFi 4e (ac1350) in terms of what hardware is available.

Alternatively, you can use a dedicated access point alongside your new router which is easier and will get you better, more up to date, technology