

Honestly, if you’re using your own router, you won’t need to worry about VLANs as long as your router separates your private network from the shared one.
For example, if the shared network is 192.168.0.0/24, you can make your private network 192.168.5.0/24 and have your router’s firewall block incoming traffic from 192.168.0.0/24. Only allow WAN traffic out, and allow return traffic.
Then have your router or connected server act as the authoritative DNS and DHCP servers for the 192.168.5.0/24 private network.
One wireless AP will be used in client mode to connect to the 192.168.0.0/24 shared network. The other wireless AP will be used as an access point for other devices to connect to the 192.168.5.0/24 private network.
You need VLANs if you want separate networks on the SAME router. But if you have separate routers, then you don’t need VLANs.
You will need two wireless access points. If the router you mentioned has two wireless access points built in, then just set one to connect to the shared network, and the other will act as an AP for your private network. Then the router can be configured to send WAN traffic out of the shared network AP.
If you use a router that only has a single AP built in, then you will need to purchase and additional AP to plug into one of your router’s LAN ports so that it has two total.
Some routers might have the ability to create multiple wireless networks on one router, but be sure the hardware can handle the load. I know my ubiquity UDM can create up to 5 wireless networks on that single device before you run into performance issues.