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You should have no problems connecting PS3 without a router.  You can just plug it straight into the modem and it works instantly.  Some models of router will actually create problems for both PS3 and 360.  I run my PS3 through a router, and to optimize it I opened a few ports in the router and set my PS3 to have priority access to them.

3 Mb/s is probably faster than you're actually going to get from your ISP, so that should be plenty.  Most routers can handle a lot more than that though, so seems like its maybe an older model.  If you don't need a router, don't buy one.