As wj says, it will be fine. It's a standard configuration for small Windows AD networks, because Active Directory absolutely requires dynamic DNS updates. You will have to decide whether you want the DNS server to handle recursion (actually resolve things itself) or maintain a valid list of forwarders (Your ISP's DNS servers, 184.108.40.206 etc.), but neither is particularly hard to set up.
As wj says again, why not just let the OS X server do it? It could do your web serving too. You would have to have thousands (or more likely tens of thousands) of clients to justify dedicated hardware for DNS/DHCP, so separating these functions is quite unnecessary -- unless you are just doing it for experimental and learning purposes.
Lastly, I recommend using a different RFC 1918
address block than the ridiculously common 192.168.1.*. The problem with that is everybody uses it and if at any point you want to VPN to somebody else's network or do something similar, that is your best bet for a routing conflict.