To add to other comments, consider a managed switch from MikroTik. Linux networking knowledge will come in handy, since their RouterOS is not especially simple but it is powerful.
I believe most of their devices jump from Gigabit ethernet to 10Gbps SFP+ ports (which you should also consider). The SFP+ ports usually support 2.5Gbps negotiation, but check the documentation. You can also buy RJ-45 Copper transceivers for the SFP+ port, although they are not cheap. Nevertheless, even including a couple transceivers, you may find something within your budget.
As for their routers, multi-port-multi-gig options are expensive so building your own router might be a good idea rather than opting for something like an RB5009, if that is what you need. Although, in a router-on-a-stick configuration, an RB5009 would be great.
Wi-Fi: yes, you can connect an access point to any ethernet port from a router or switch. They often come with PoE injectors.
Consider TP-Link Omada access points. If you need multiple access points, they suggest running a controller, it can be installed as a docker container. MikroTik has access point options but my experience with their old wireless options left a bad taste in my mouth. I hear the new wifi-wave compatible hardware is good, though. Any device running RouterOS could act as the CAPsMAN (AP controller)
To add to other comments, consider a managed switch from MikroTik. Linux networking knowledge will come in handy, since their RouterOS is not especially simple but it is powerful.
I believe most of their devices jump from Gigabit ethernet to 10Gbps SFP+ ports (which you should also consider). The SFP+ ports usually support 2.5Gbps negotiation, but check the documentation. You can also buy RJ-45 Copper transceivers for the SFP+ port, although they are not cheap. Nevertheless, even including a couple transceivers, you may find something within your budget.
Using a router-on-a-stick configuration, consider a CRS305 (4x 10G ports and 1x Gigabit port) or a CRS309 (8x 10G ports and 1x Gigabit port) switch.
As for their routers, multi-port-multi-gig options are expensive so building your own router might be a good idea rather than opting for something like an RB5009, if that is what you need. Although, in a router-on-a-stick configuration, an RB5009 would be great.
Wi-Fi: yes, you can connect an access point to any ethernet port from a router or switch. They often come with PoE injectors.
Consider TP-Link Omada access points. If you need multiple access points, they suggest running a controller, it can be installed as a docker container. MikroTik has access point options but my experience with their old wireless options left a bad taste in my mouth. I hear the new wifi-wave compatible hardware is good, though. Any device running RouterOS could act as the CAPsMAN (AP controller)