How to set up an access point with controlled traffic

Dear all,

I have been asked to install a wifi access point in a conference room, where there is already a 300/300 fibre network connection, but managed by a private supervisor on which it is not possible to intervene in any way.

The access point should provide wifi connectivity to about fifty people (max) distributed over an area of about 200 square metres.

The connectivity, however, should not be open, but allow navigation ONLY on a couple of institutional/governmental sites plus access to the Play Store of Google, Apple and Microsoft for downloading updates of connected devices.

Trying to figure out the problem, I realised that there is NO Access Point device on the market that can profile traffic as required, so I think we need 1) a firewall + 2) a managed switch (VLAN) POE + 3) a wi-fi antenna.

1) FIREWALL ???

2) GS308EPP - Switch PoE + Plus Gigabit Ethernet, 8 ports (123 W)

3) WAX620 - Access Point Tri Band Multi-Gig PoE AX3600

I wanted to know if this is the right idea and what products you would recommend to implement this project.

The budget is quite limited (< 500$ possibly)  and it would be great to have all NETGEAR devices.

What about the Firewall??

thank you