A small Cisco 800 series ethernet router would do the trick. They can be configured using a web interface if you are not that good with the CLI. All you need to do is configure the router with an ip address on each subnet and it will act as the gateway between the 2 networks. Routers also isolate broadcast domains so your users network wont get swamped by traffic from your machine network. To keep costs down have a look on eBay.
Another option to look at as well is to potentially enable routing on your managed switches, assuming they support layer 3 routing.