Scook has given good advice.
The external interface is the best option. Just be sure it uses native ASIO drivers. Some of the cheap ones don't. You should be good if you follow the advice in post 14 for the brands to choose from. I personally have used a Focusrite for many years and love it.
Once you have a good interface handling the audio in and out, you may be able to use the USB port on the amp to connect it directly to the computer. You will need to experiment with that. Most interfaces I have seen only have one USB port for their connection to the computer, so I doubt you will connect the amp to the interface in that manner. I believe keyboard players with USB ports on their synths are able to input in that "direct to computer USB port" manner without issues so you should be able to do likewise with the amp/audio. Since all audio will be handled by the interface using ASIO, the whole MME/WDM issue will be a thing of the past.
One suggestion, get an interface with phantom power and buy a decent condenser mic as well as the interface. This will make recording vocals and miking the guitar amp easier. Using a dynamic mic isn't really the best way to go but if money is tight, you can mic the amp and vocals with any dynamic to get started. While vox and miking electric guitars are fine with a good old SM 57 dynamic, if you need to mic acoustic guitars, a condenser is the tool for the job.
As far as inputs go.... MC only allows 2, and most interfaces in the lower price range also only have 2 inputs.... if you need more, or are thinking of upgrading to X3, then save the money to buy the bigger interface. I have done everything I have ever recorded using only one input live out of the 2 I have. Since I'm not in a band or running a studio for hire, having two inputs suits me fine.
hope this helps a bit.