Don't always assume the extra IP costs. I have three, and when they assigned them, they told me me they MIGHT charge an extra dollar or two per month for the extra IPs. They didn't. This is DSL, and not ohne of the big providers, but still, if you ask the right perso nicely, sometimes you will get a favor.
As to whether you want to go wired or wireless, hub or switch...
Here's how it works. A hub and a switch are largely the same from your perspective. They both allow you to have multiple network devices connect together in a single network. Netwoprk devices in your case are three -- the cable modem, the gaming PC, and the "utility" PC. You can't completely separate them, unless you get a second cable modem. Even then, they will still really be on the same network, because the cable company itself provides a single network segment for all users within a particular area.
Technically, a switch is used to isolate connections among any two random devices. So, traffic directly between the two PCs will not affect available network use of a third device. Since all your traffic will be between the modem and either PC, it makes no difference. Since a hib is cheaper, you would go with a hub over a switch.
Now, as for wireless... the equipment is significantly more expensive. The wireless equivalent of a hub is an access point, or AP. The AP is a network device, just like the cable modem and the PCs. It needs to connect to the cable modem in place of a hub. It and the cable modem could also be connected to a separate hub (to allow wired/wireless flexibility), or you can get a "wireless router" which combines an AP wired into a hub/switch in a single unit.
An AP will run you $80 to $200. A very good home wired hub will be less than $60.
A standard network card (NIC) can be had for $15 to $40. A wireless card is $65 and up. Plus, you almost certainly have a wired NIC for the PC that is already hooked up -- and the second PC may have come with an Ethernet NIC built in. If that was the case, you would need no new equipment on the PCs for wired access.
Finally, wired networks tend to require very little set up beyond getting the wiring in place. Wireless networks usually involve more software setup and AP setup, especially if you want to avoid security problems (i.e., someone examining your network traffic from the outside, or illegally piggybacking your cable modem connection).
So, let's compare potential costs:
All wired: $45 hub + $0 new wireless NICs + (guess) $120 to wire up = $165
If need to purchase a new NIC add $20, for $185
If using wirless for both PCs:
$90 AP + $150 wirless cards (2) + $0 cofiguration headache unless mental help later required = $240.
If using wirless only for the new PC:
$140 AP with hub built in + $75 wirless card +$0 configuration but still need to buy bottle of aspirin = $215.
So, wired looks cheaper than wirless no matter how you put it, although it could be cheaper if you had a complex cable run, or if you added additional PCs later. Plus, wirless is a more flexible. Plus, wireless is cool (if not as reliable).
Note: If you do get a router (wired or wireless) at some point, you will probablt want to set it up so that your gaming machine is the "DMZ" machine. That will involve assigning it a permamnent IP, and setting that IP on the router setup to be DMZ. Otherwise, the firewall protection that all today's SOHO routers provide will block the gaming network connections. Get ZoneAlarm to provide software firewall protection.
Personally, I like wireless. The added expense and headache are worth it for the flexibility. Ihave a three pound laptop with a three hour battery and a wireless card. It is absolutely so convenient to find a quiet spot in or around the house and get stuff done n the laptop. There is really no way I could get that with wired, even if I ran dozens of drops and had retractable reels at each drop.
But, in your configuration, I have to believe wired wins. I think not having a router is a mistake, although initially I would set up the router as a simple hub (i.e., pluf the cable modem into a "LAN" port instead of the "WAN" port). It gives you the flexibility of changing to a more sophisticated configuration later, without having to buy new equipment. A cheap SOHO router is not much more expensive than a good hub today.