I'd probably advise against getting an external drum machine.
The drawbacks are that you're stuck with whatever sounds are built into it.
There's usually several drum kits to choose from but they're limited.
Compare that to something like the VST LM-4 or even better, Battery.
You can use any sound you want off your hard drive. So you can go online and find .wav files of different snares or cymbals etc. You can also program Battery so that you have 10 different variations of the same cymbal...depending on how hard you want it to be hit.

Another drawback to external drum machines has to do with how audio is recorded on the computer. With an external machine, you'll have to convert the midi to audio in real time. In other words, playing the song from beginning to end for 4 minutes or whatever.
With a VST drum machine, you just have to export the sound, which means you can lay your audio drum track down in a matter of seconds.

Last but not least, the drum sounds on those Boss Dr. Rhythm things are really cheezy.
I've got a Boss Dr. Synth with the same drum machine and I wouldn't dream of using it except for practice.

The amp I'm mentioning is for playing back your recordings.
To be able to properly mix your tunes you'll need the equivalant of a stereo system with some decent speakers. Or in other words, an amp and a pair of monitors. This will also give you a headphone output that has better sound and more bass than the one from the mixers headphone output.