Tullphan, in addition to what's been posted here's what I'd recommend based on my experience:
1) Use ZoneAlarm instead of Sygate. While they are both decent products, from the sound of things I think ZoneAlarm would suit you much better (and I have never been hacked with ZoneAlarm, but I have with Sygate, by the by)
2) While it is true that you cannot technically "share" an internet connection using the Linksys "Network in a Box," (as you could as described in #3), when I had DSL and I had the same Linksys switch I found that it was actually possible to use the same username/password to sign on several computers at once. My setup was as follows: RJ-45 cable connected from wall outlet to modem; CAT-5 cable from modem to uplink port in switch; CAT-5 cable run to each of 3 PC's using the remaining ports. (my DSL provider was Verizon, fyi)
3) If you can't get that to work, get the Linksys Cable/DSL router (BEFSR41). For about $60 all you have to do is plug in the CAT-5 from the modem to the uplink port, plug in each PC as before, only this time the router does almost all of it's own configuration for itself and each PC automatically, it literally "shares" the connection using something called NAT (network address translation). While you still only have one DSL account and username/password, the router will act as your own internal server for all the PC's connected to it. (I had it up and running out of the box with just the quick setup card in about 5 minutes).
Good luck!