How to use different DNS forwarders based on the source IP or MAC

First, yes, you need your own nameserver for that and bind is as good as any. Maybe a little harder to get into at first, but there are enough examples and tutorials on the internet. The advantage with bind is, that you probably won't ever miss a feature.

I suppose you are using DHCP to provide all your clients with IP Adresses and such. One of the options you can provide via DHCP is the search domain (not sure on the precise naming). Computers store this information and whenever a computer cannot resolve a name for instance movies it appends the search domain, for example home.sweet.home.org and tries again with the full name movies.home.sweet.home.org. Using your own nameserver and DHCP allows you to use short names, if that's what you're looking for.

However, you may run into problems as bind will not resolve names to a combination of ip and port. If you can't separate your web interfaces via virtual hosts (if you're using apache) you may need to give your media server multiple IPs and have those services listen on different IPs.

Setup a separate server to act as a resolver. I'd recommend any unix running bind. Then have that server forward internal domains only to 10.1.1.1, while resolving everything else the normal way.

There are instructions on how to make bind do that at this question.