IP network addressing, VLANs, and Internet access methods are three different animals.
The KISS strategy (Keep It Simple Stu**d) is the best strategy.
The wireless LAN can be a separate IP subnet (a.k.a. VLAN) or subnets. This is preferable.
I would not recommend DHCP for some stations, and not for others. Make all or most clients DHCP addresses. This is an old and accepted practice.
DHCP is great at handing out addresses automatically and managing them. Routers are great at creating and maintaining VLANs.
Keep it simple. Do not implement solutions that only address one current issue. Eventually you will have many solutions to many problems, all trying to inter-operate. It can be a mess and can introduce entirely new and unexpected problems – costly problems.