A four-year-old dell should have a USB keyboard and mouse (the connector looks flat and thin). These will work on any computer. Your monitor is likely VGA (plug has a blue face), and is the only common monitor connector; every computer you are likely to buy will be able to use it. Therefore, don’t worry about replacing those. Just replace the main part, the box. The new one will likely come with a new mouse and keyboard anyway, but if you like yours better, you can still use them.
It sounds like you’re not a heavy power user, so don’t bother looking for the latest and greatest. It is very likely that with the new year coming up, right after Christmas you can probably score a deal on a last-year’s model low end machine for not much money.
Look for a computer that has the i3 processor from Intel, and at least 4GB of memory (RAM). Also, it should have Windows 7, but not the “Starter” edition; don’t bother with the “Ultimate” edition though unless it isn’t going to add to the cost, because you won’t use most of what the “Ultimate” version can do.
Brand is pretty superfluous for the level of computer you want, but try to get one with a recognizable name. HP, Dell, Gateway, Acer, Asus, all these are good, reliable machines that will (probably) use fairly standard hardware and a decent hard drive.