Network setup is pretty simple in terms of basic networking. There are three main components in a small office network, the router, the modem, and the switch (if necessary). In simple terms,
The modem which is from your Internet Service Provider. E.g. DSL/RoadRunner. The modem connects you to the Internet.
The router acts as a gateway for the other computers/devices on your network. It assigns addresses to the local computers and acts as a firewall in a basic network.
The switch is like a giant splitter. Which basically balances traffic between the connected devices. You'll see the mention of gigabit often, that's an indicator speed.
Typical layout is: Modem <- Router <- Switch <- Computer
With SBS 2003, the server handles addressing and DNS requests. Think of DNS like a phone book. When you type in a name like google it gets translated into a number called an IP address. This occurs behind the scenes. As Bert always says, if it's an issue with SBS, it's almost always DNS. This happens locally too when sharing files. If I look up VICKISERVER (which AC does a lot), it gets translated into an IP address (192.168.X.X). If there's a problem with the DNS server (phone book), it can take a long time find the desired IP address ("phone number") which results in long loading times.
Just as a side note, have you tried disabling hardware acceleration on the client computers? I noticed you mentioned issues on imported items and the RX Writer screen. Instructions are in my signature.
As for the cost of a new server, many sites offer financing that will let you pay off the bill with a monthly charge if you truly believe the server is the problem. Some even have no interest if the sum is paid ins 6 months.
As a side note about gigabit: Gigabit transfers at about 125 megabytes/second (more than enough to max out a typical hard drive) and 100 Megabit (typical) transfers at about 12.5 Megabytes/second. For a 10 fold speed increase, it's usually 20%-50% more than a non-gigabit switch. If your II are large, then you should probably use gigabit. If not, you should still use gigabit.