Yeah it has the Ethernet input, but like other basestations, it doesn't have a way to also have another Ethernet output but many people don't have a use for that. For example, to bring another computer onto the network that doesn't have a wireless card. And yes you can have 3 users with the Airport Express, up to 10 users without a problem.
I think it's up to you whether you go for the Airport Express or the Linksys router. With AE, also get a wireless connection to your stereo, and a beautiful, Apple-branded product. With Linksys, you get no stereo connection, an ugly router, but you save some money. But, like I said, I have my Airport Express and have had any problems and enjoy very much. I have not tried the Linksys routers, so I cannot provide any real opinions on that.