If I do this, what sort of midi engine will I have to get to get it running? Is this a software thing, or some outboard gear? I know absolutely nothing about midi...
You don't need a midi engine as such. Your computer knows all about it. If you get something like Musicworks or Sibelius, your PC can translate their internal midi commands and play them via its own soundcard. As I mentioned above, this may not sound very nice, but at least you will get an idea.
I am not familiar with Soundfonts, but if it needs to be loaded as a VST instrument, then you will need something that will host this instrument, which means a music program such as Logic, Reaper, SOnar or whatever, which then introduces another level of complexity.
If you are not familiar at all with midi, then a good way to come to terms with how it operates is to think of music boxes or old player pianos. You can think of midi as a set of instructions that tell a device to play notes of various pitchs, lengths and intensity; the same way a paper piano roll 'instructs' a piano what notes to play.
More elaborate player pianos exist, e.g. the orchestrion, which is a "player piano that is outfitted with additional automatically controlled instruments such as pipes, xylophones, drums, cymbals, glockenspiels, triangles, wood blocks, tambourines and other instruments and effects."
If you think of the orchestrion as your computer's soundcard, then midi is the means of communicating with this, which you can via a keyboard, or via notation software, or via the midi facilities of more general music production software.
There are alternatives to your internal soundcard. One is to use an external sound library, and the other is to use virtual instruments, as legionserial intimated.
Do you need to know about midi? Well, not really. For example, when making a player piano work, you don't need to know about its internal machinery. You just need to know how to load the paper roll and set the thing going.
However, were you to aspire to greater sophistication, and seek to modify the actions of your orchestrion, then you would need to know the internal workings. The same applies with midi.
I suggestion a search on the web for notation software; there may be something freely downloadable, and have a play with it.