Throughput is the amount of data that can move through your LAN card. Proper throughput settings allow for the maximum level of transfer speeds as supplied by your connection.
Bandwidth is the speed which your ISP supplies to you.
Yes, if you are paying for 3Mbps, that's what you should be getting.
Most of today's current routers and modems are fully capable of giving you the maximum performance available from your ISP.
Here's an excellent broadband speed test: Speedtest.net