Ian, been there done that. Several times. (The wireless network, that is, you can keep the hail holes in the roof... )
You will need a device that will be the primary access point. It is the interface between the wired network and the wireless clients. The USB devices you referred to are all clients, not access points. They plug into the USB port of any computer and thereafter that computer can get onto the wireless network through the existing access point. In essence, it is an easy way to incorporate wireless capability into a computer without opening the case - just plug in through the USB port. Thus, that idea won't help you.
So what are the options? You mentioned a base station - that's your best bet IMO. But first, the alternatives to a base station. There are only three devices I've stumbled on out there that could serve as a plain access point node when plugged into a port on your wired network. The DLink 900AP or Belkin F5D6130 are both 802.11b (i.e., too slow when you've got a fast g card in your notebook); and the Belkin F5D7130 is g, but it costs more than a standard base station so why bother.
So you're back to looking at base stations. Without knowing more about the wireless card in your notebook, I'm hesitant to suggest any particular brand. Unfortunately, there are some monstrous incompatibilities between some of the different devices, despite having advertised "compliance" with the 802.11g standard. There are two principal suppliers of the chipsets, Broadcom and Atheros, and you are usually better of if you can keep both ends of the connection using the same chips. Do you have any idea who the chipset maker is on your wireless card?
Once we figure out which base station to get, you will need to reconfigure your network. If I correctly understand your setup, the ADSL modem you have not only brings in the public IP, but does some network address translating (NAT) and can route to multiple inside clients who are issued non-public IPs in the 192.168.1.xxx range. However, it only has one ethernet jack on the back of it, so it can only physically service one client device. You have it connected to adapter #1 of the gateway system.
You then use ICS on the gateway system to do a second layer of NAT for the rest of the home network using the 192.168.0.xxx address range. You didn't say so, but I'm going to guess that you have a hub or switch attached to network port #2 and that is where the rest of the home network branches out from?
If I have imagined your setup correctly, first off, you probably don't need the gateway system to run ICS and a second layer of NAT - if the ADSL router indeed does DHCP to the full range of 192.168.1.0-255, then you merely need additional ethernet ports for the additional client systems elsewhere in the house. You can achieve that simply by connecting the single LAN port on the router directly to the uplink port on your hub/switch. All your client systems will pull their own IPs from the ADSL router (in the 192.168.1.xxx range) and the hub/switch will handle the distribution of the packets to the specific destination system.
So where does a new wireless base station fit in? The typical base station has 3 functional aspects - first, it takes an incoming single IP address and does a layer of NAT to multiple clients which have been issued inside IPs through its DHCP service. Second, they all have an integral switch with 4 or more additional ethernet ports. Finally, it manages the wireless system, issuing yet more inside IPs to all the wireless clients. So it could effectively replace the DHCP and NAT component in the ADSL router, plus replace your ICS system, plus replace the hub/switch from which your home network emanates.
Depending on the specifics of the ADSL router, you might be able to set it to plain bridge mode, which would turn off its DHCP service and the first layer of NAT. Thus, all DHCP/NAT and distribution (both wired and wireless) would be handled by the new base station. If there is no way to set the ADSL router to plain bridge mode, that's okay - let it feed 192.168.1.1 to the base station as the single incoming IP rather than the public IP issued by your ISP, and everything else is as already described - except that you will need to be sure when configuring the base station that you set it you use a different range for its DHCP; a minor undertaking, but a nuance that will cause it all to fail if you don't set it right.
Once you get the wired network running, then you introduce the wireless client to the base station and tear your remaining hair out getting them to cooperate.
This is probably enough to start with tonight. Let me know if I've imagined your current configuration correctly, as well as additional info on the wireless card in your new laptop. We can go from there tomorrow...