You do not need RSLinx Classic Gateway or FactoryTalk Linx Gateway. Both of those are special-purpose software that bridges communication driver configurations like DH+ and serial or OPC and FT Live Data, rather than general purpose network devices.
In general, you need a VPN or other general purpose network bridge to allow access to the network to which your machines are connected.
Part of configuring your PLC and HMI will also be setting the "default gateway", which will be the local network IP address of whatever router or VPN appliance you use. If you have a DHCP server, it may already be giving the devices its own IP address as their default gateway.