Instead of Untangle, I suggest using a fully-featured server-class OS like FreeBSD or OpenBSD (or Linux, but I prefer BSD for firewalls). You'll end up with a much more configurable and powerful system that you can use in a pinch as a filserver/NAS or simple web server, or HTPC, or any number of other things. But Untangle doesn't look like a bad option, if you decide you prefer it.
Your cable modem will almost certainly not use Gigabit Ethernet; a regular 100Mbps Fast Ethernet connection will serve it just fine. Of course if you're buying a new separate NIC, you may as well buy gigabit anyway, but if you have a Fast Ethernet NIC built-in or lying around, there's no reason not to use it. You will want gigabit for the LAN side, if you intend to use the server as a fileserver or NAS or provide any kind of bandwidth-intensive service to the LAN.
Using your existing wifi router might be somewhat problematic; not all of them play well with others. If you are using BSD, one thing you can do is buy a PCI or PCIe wireless card and install it in the server, then configure it to run as an AP. Your BSD box then becomes the wireless router. If you like your current wireless router, you can just connect it to your LAN and have it act as a dumb bridge (i.e., not using any routing features). Usually this doesn't require any extra setup, just not using the "WLAN" or "uplink" port on the router.
As for the LAN side, your gigabit switch will not have an "uplink" port; if it does, it's not a pure switch. All the ports on the switch should be equivalent. Here's how I'd wire the whole thing:
Cable/DSL modem <-> Fast Ethernet NIC on server
Any gigabit port on switch <-> Gigabit NIC on server
Any gigabit port on switch <-> Another computer on the LAN
If you use a separate wireless router:
Any ethernet port on switch <-> Any non-uplink ethernet port on wireless router
If you use a wireless card in the server in AP mode, you just need to configure it properly, and do not need any additional hardware. If you set things up properly, any computer on the LAN will be able to communicate with any computer on the wireless network.
If you're interested in more details about the Linux/BSD option, just mention it or ask another question and I or someone else will be more than happy to explain.
EDIT: I realized I forgot to address your question about performance. I can't speak for Untangle, but a BSD-based setup will be able to handle a typical home LAN (~5 computers behind it) on just about anything: my gateway/server used to be an old Pentium II box I had lying around, before I moved it into the 21st century last year. A dedicated firewall/personal server can run on just about any old hardware you can get your hands on, or the very cheapest modern servers you can buy.