Ethernet splitter

There's nothing called a "splitter". There are two different things: a hub, an a router.

A "hub" is a device that connects multiple network interfaces together. If you connected your DSL modem to a hub, each computer connected to the hub would try talking to your ISP, fetching IP addresses, and whatnot. Your ISP probably won't allow that. However, a hub is useful as a "splitter" of sorts in that you can connect one port to a single network connection and have multiple additional ports.

A "switch" is like a hub, but instead of broadcasting all the network traffic to every port, it copies traffic only to the machine that needs to see it. This can speed up busy networks.

A "router" is like a hub with a built-in computer that acts as a firewall, gateway, DHCP server, etc. It's what people generally use in a household where they are using wireless or multiple computers within the house. A typical setup would plug a wireless router (which usually still has some wired ethernet ports on it as well) into a DSL or cable modem, and have all the computers within the household connect through it.

J D did a very good job of describing the pieces of equipment. What you want is an inexpensive router.

Connect the DSL modem to the WAN/Internet port on the router and connect the AirPort Express (AX) to one of the LAN ports on the router. Configure the AX so that the option to distribute IP addresses is DISABLED. This will allow your wired iMac to use the printer attached to the AX.

The AX does not support wired clients. Therefore the only way to connect a wired client AND the AX to your internet connection is to put a router (with 2 or more LAN ports) between the internet and your AX.

Your wireless connection is probably several times faster than your internet connection. So you won't gain any speed by switching to Ethernet.