A printer which already has network capability (i.e. has an ethernet port and can be addressed via TCP/IP) can be connected directly to your router, but will require setting up (I have not done this myself but know it has been / can be done).
Otherwise you will need a print server to be connected to the router.
Choice of 3-in-1 printers? You mean a combination printer/scanner/fax? Look up reviews in magazines or web sites, then/or post in the Consumerwatch forum.