Have you ever used OpenMPT? I'd sort of like to get into that but I'm not sure it's right for me; it seems complicated and I'm not sure I'll like all the sounds it has to offer. This, and other MIDI programs like it; can you record your own sounds into it? I'd much rather make my own sounds then emulate other sounds like NES sounds.
I have used it; it's okay but it takes some configuring to make usable (I don't like its default keyboard setup at all). That said, it's a fairly solid tracker; though there may be better ones out there. Tracker formats generally have a pretty distinct sound. Trackers give a lot of control, but it's complicated to get good at and if you want things that don't stick to a very rigid timing grid, you'll have to get comfortable with learning about how the tempo is calculated and how ticks relate to that.
Recording your own sounds depends very much on what program you're using. Generally, yes, most trackers (OpenMPT is an example of a tracker; generally, trackers include any program with its sort of interface for music writings, although of course there's plenty of variation on the specific implementation) allow this. This is definitely true for .mod, .xm, and .it files, all of which I'm pretty sure are supported by NeoLemmix.
Some trackers are designed for specific sound chips, though, and therefore don't have this capability (e.g. FamiTracker produces NES music; Adlib Tracker 2 makes OPL3 music; these programs can only take instruments that the hardware they write for supports - trackers of this type can either be runnable on the hardware they write for or they can use emulate the sound hardware: Adlib Tracker's a DOS program, although a functional windows port that emulates the OPL3 exists, whereas FamiTracker is a Windows program that emulates an NES (but is capable of exporting files you could play on one if you had the hardware to do so)).
If you ever decide to get into chiptune production, most methods of producing them use either a tracker interface or MML, and MML is very difficult and involves files that look like this:
A o2 @v0 @1 l4
A r1r1r1r1 L @q0 @v1 o4 @1
A |:[[c4&c12<g12>e-12]2 c4<g2> | {ce-g}b-2a-4&a-12g-12a-12g1]2 <{g>ce-}4g4&g12g-12a-12g8e-8<{bg>e-}4 c1:|2
(taken from a cover of Link to the Past's Death Mountain theme. Can't remember which part this corresponds to - this isn't the full file and doesn't contain all the information that would be needed for it to compile)
I've messed around with MML a bit but find FamiTracker better to use for NES covers.
I'm doing this with hardware and real-time recording, as such my songs may not always bee 100% spot on, but I think that adds "soul" [actual explination: I'm too lazy to spend more time on it to get it right].
Also I should point out I'm not looking to make exact remakes, I'd like to put my own spin on them when it feels right.
This isn't necessarily bad, but a word of caution:
If it's not 100% note-accurate, it'd better be obvious that it's not intended to be 100% note-accurate.
An analogy:
Animated films (most styles, incl. anime, Pixar-y stuff, old Disney animations, etc.) can look nice and be a fantastic viewing experience! But once they look too realistic (e.g. 2009 film adaptation of "A Christmas Carol" - they went to such lengths to make it look realistic, including basing everything off of real actors' performances, that you have to wonder why they didn't just use live action with a little bit of CGI when needed) the fact that they aren't quite perfect begins to detract from the experience and just makes you wish you were watching something that wasn't animated.
To bring this back to music, it's like the difference between listening to someone play a song in a different style than it was originally written, vs. hearing someone play the song as it was originally written but with a few noticeable wrong notes in there.