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.