your connection most likely doesn't show in the system tray because the box isn't checked to enable it to be shown. right click on my network places and goto properties. then find the wireless connection icon and right click it and again, goto properties. the window should look like the picture. check the box at the bottom to show the icon in the "notification area" when connected.
as for the access point, i would recommend the Linksys WAP54G model. Easy to configure (almost as easy as out of the box) and it's a very reliable product for home users.
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