Maybe a step back given the "ELI5".
First: what is MIDI?
It's basically a digital form of music notation - a stream of commands telling whatever is playing it which instrument is playing what note(s) at what volume. Very storage-efficient (extremely important when hard drives were much smaller than the storage on a CD) and flexible - which is why the music industry used it.
That means that the basic melody will be the same regardless of what you play it back on, but the sound can (and will) differ very significantly. In the early days of MIDI there was no standard for which instrument mapped to which MIDI code, so games had to specify the exact device to be used for playback (Roland's MT-32 was the most common). From the early 1990s onward, the industry converged on the "General MIDI" standard, which at least standardized the instruments so you could just compose for GM. Even so, tunes will sound different on each playback device and to get the sound the way the composer intended, you still want to find the same device they used, or something using the same sample set. Specific hardware matters. A lot.
Then regarding that hardware - fundamentally you need two things:
- a MIDI interface that gives software something to talk to. The standard here is MPU-401, from the Roland interface card of the same name. Most sound cards had an MPU-401 compatible interface built in - but not all, not all features of the original Roland MPU-401 were supported and in some cases (most famously on all the Soundblaster 16 cards) it could be buggy. Separate MPU-401 compatible interfaces also exist, both vintage (the MPU-401 itself and MusicQuest clones) and modern replica (HardMPU)
- a MIDI synthesizer that turns the codes it gets from the MPU-401 over the MIDI interface into sound. This can be onboard on the sound card, it can be an external module (=box with at least MIDI in port and audio out) or it can be a "Wavetable" daughterboard that connects to the sound card via Wavetable header. Potentially it could also just be software; Windows includes a software MIDI synth, as do various card drivers. This is one of the reasons dedicated hardware MIDI synths started disappering after the mid 1990s. Unfortunately, software MIDI synths aren't an option under DOS.
Your first choice should be what kind of MIDI playback you want. Basically 99% of people with MIDI hardware back in the day had cheap nasty stuff that didn't sound too good. But if that's what you played on, you could be nostalgic for it. Even if you didn't, to get the real 1990's experience, you'd want something like that. Alternately, you could be looking for the best MIDI sound exactly as the composers intended. That's not as hard as it sounds, as basically everybody composing for games back then used the Roland SC-55 module, so getting something that sounds just like it would do the trick.
Then you should choose what form factor you want it in - on the sound card, on a Wavetable daughterboard to stick onto the card, or an external module.
- Getting it on the card is the simplest option, but the most limited, and if you want the high-quality stuff, the cards with something like SC-55 sounds can be VERY expensive - and even lesser cards with onboard wavetable aren't likely to be cheap. Moreover, you need an ISA bus for this option, as PCI cards with onboard wavetable that will work under DOS are basically non-existant.
- Wavetable daughterboards used to be very expensive and hard to find, but if you're willing to go for modern replicas, Serge has affordable, available options, both for 'authentic' crappy stuff and the Dreamblaster X2GS which has official Roland sound banks. Downside is that you need to open up the case to swap daughterboards
- external modules look really cool and offer a lot of flexibility: you can easily hook up different ones, and Serge (same link as above) even has an enclosure to turn Wavetable daughterboards into standalone modules. Downside is that these things can be pretty expensive, as leileilol already hinted, there can be hardware/battery issues and they take up space.
If you really don't know, I'd probably recommend going with Wavetable daughterboards as the sensible option. That means that your sound card will need to have a Wavetable header and an MPU-401 interface, preferably not buggy.
Fully agreed that ISA is best, but even if you don't have an ISA slot, there are better options than SB emulation on a live/audigy, specifically ones that would support wavetable daughterboards.
One to look at in that case is the ESS Solo chip, one of the least troublesome PCI chips under DOS. Moreover, at least one card - the Terratec Solo-1 - is widely and cheaply available and either come with a wavetable header, or one can easily be added (it's literally as simple as soldering the missing 26-pin header block, no further hardware or software modifications needed).
If you do have an ISA card, you have *lots* of options. My only recommendation would be to steer clear of the Soundblaster 16 (and AWE32) models with all their bugs. You also don't need SB16 as you can always fall back on the emulation from the Audigy there. I personally like cards based on Aztech AZT2320 chips as a low-cost, easily available bug-free option, but there are equally effective options with chips from Crystal, ESS, OPTi and Yamaha. If you have two ISA slots you could also consider a standalone MPU card, although it will increase cost, but let you use sound cards without good MPU-401 and/or wavetable header.
So, tell us more about your system and its slots, and what type of MIDI devices you'd want, then we can give more specific tips.