I understood you have an autonomous 1250 AP. right?
From what you described (no vlans, the AP have an IP, WPA-PSK is going to be used) I think you are on the right track.
If you create -correctly- an SSID on the AP it should give you wireless connection to the same network. Clients will get IP addresses from DHCP on same subnet as the BVI interface on the AP (DHCP scope supposed to offer IPs on same subnet).
Why don't you give it a try? or you did and you have any problem?
Let us know if you get any problem so we see how can we help. But from your description above I am expecting it is going to be OK.
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As you mention you have a flat network where all devices and users are on the same subnet.
In this case on the AP you will just need to give the unit an IP address, configure the SSID, the encryption method to use and then if you want to broadcast the SSID select the option of guest mode (which does not mean guest access just that it will be broadcasted the SSID).
So in other words the configuration you mentiond should work.