Like others said, Burialesque music is best done in a DAW, chopping up samples, pitching them up/down, making basses/leads/glitches out of sample snippets from game music or classical orchestras, and of course some mangled r&b vocals or movie quotes. Believe me, I tried with hardware but came nowhere close.
With Ableton and samples I got this (my best result, I think, although my mixing/mastering skills weren’t that great at the time - still aren’t)
Except Burial doesn’t use a DAW. But since the OP already has a DAW they can use the built-in audio tools for sample manipulation and FX processing.
Here’s the very long interview with Burial.
After relistening to burial early ambient tracks they seem very loop-ey.
Seems like burial is reversing and timestretching several loops without a grided structure to the tracks. I guess a sampler/looper with heavy FX/timestretch could work as a piece of hardware?
I think it’s less about the specific tools and more about the feelings and emotions that’s he’s trying to express. To get as close to what I think he described of his process in that interview without resorting to an old copy of Sound Forge I’d recommend a free audio tool like Audacity.
You can already do all of this using Ableton Live though in my opinion Live can be a bit heavy handed for certain things. There’s a direct rawness in how Audacity is visually laid out that may make it feel a bit more freeing in order to roll out and arrange audio. But both tools allow you to take audio and make one-shots or loops, etc. and arrange them as you see fit.
Any ‘time-stretching’ done by Burial appears to be done is a raw/intuitive and maybe to some primitive way, perhaps by dragging endpoints to fit the space? I don’t know for certain. He’s looking at waveforms, not at note data like one would do in a MIDI sequencer on a DAW.
Turning off the grid in a DAW-piano roll really helps with getting that loose feeling/vibe
if you can trade model:cycles for model:samples, you would be pretty much set for making the type of music that you want.
Volca fm2, albeit without interface, is still 6 voices of nice sounds.
which can go into 
korg nts-1 is the king of affordable and diverse FX, great little thing.
and after its properly wet with FX
model:samples can mangle those sounds into delicious ambient.
Minilab 3 can control both, volca and samples 
Fraction of your budget can go into getting a small field recorder, to feed model:samples some non synth textures. (perhaps Tascam DR-05)
Reaper is excellent for audio editing and manipulation, you can set up your keyboard commands to quickly reverse/normalise/stretch sounds and apply whatever FX you want. I would strongly recommend it over any standalone audio editor at this point, with the exception of software that has hi resolution spectrograph views. Reaper has a spectrograph view and edit mode but the FFT resolution is lacking meaning low midrange and below content is pretty indistinct sadly, it’s still nice to have though and has been useful for quickly finding particular transients.
It’s taken me an embarrassingly long time but I’ve fallen head over heels with REAPER. It’s just soooo damn good. It’s brought me back to using the computer for music again.
That said, I didn’t realize that Audacity has time stretch, called ‘Sliding Stretch’. It’s cute.
https://manual.audacityteam.org/man/sliding_stretch.html
Excellent, sound advice. Though for more always-with-you immediacy, the OP could use Koala app that’s already on their smartphone rather than a field recorder.
Thats a great suggestion! Depends on the phone but some of them sound just as good as a small field recorder.
I struggle with the VOLCA FM2 as I find its sound very “cold”. What I like about burial sounds is that they seem warm, almost organic…
I wonder if this is FX related, or just a mater of sample quality, or layering different textures…
The model:samples seems to be designed as a sample based drum machine, would you say it is good at doing ambient?
I guess I could pick that, or a second hand digitakt (but seems to be a drum machine as well?) Or a sp-404 mkII…
I’ve always loved my ‘crappy’ mic (and speaker!) on my various mobile phones. I used to have a fairly high-end field recorder with XLR jacks, etc. but found that when I wanted to capture sound in the moment I often didn’t have it with me. For field recordings (in the city at night or in the forest or at the beach) what I’m really trying to record is ‘air’, to get a sense of the vibe of the place and fidelity is not the highest priority.
one of the great things about all 3lektron boxes is how flexible they are. digitakt for example is labeled as a drum computer but it’s a sampler with flexible envelopes. has nothing really to do with drums specifically apart from the labeling on the trig’s, and the samples it come pre-loaded with. tho it is great as a drum machine.
all ov em can do ambient really well, including model samples.
Burial’s music sounds the way it does because he’s using a lot of samples from music/games/etc that already has a lot of ambience to it, when you slow that stuff down and put multiple layers of it together you get rich fuzzy harmonics and a nice warm tone, and I think it’s case of smart filtering and frequency bracketing to keep it from getting too muddy. Probably the mastering Hyperdub put it through helps a lot too.
FM synth programming is entirely its own thing. It is possible to make the Volca FM sound very warm and organic, but it does take learning. The Oscillator Sink series on the subject available on YouTube are excellent. He also offers free patches if you don’t want to take the trouble of programming them yourself.
Impulse response reverbs are worth experimenting with too, you can get a nice natural sound with those.
Listening back to some of Burial’s stuff he’s definitely making heavy use of filters to roll off top end or cut the lows for different sounds, and bandpassing certain elements to isolate something so it sits just right in the mix -
(Early unreleased track, sadly very low bitrate but that crust probably adds a bit of pirate radio vibe to it tbh).
Also plenty of compression/saturation is essential for warming things up, probably a lot of the sounds he’s using are already fattened due to being in released music/games/film, but if you’re using bits of field recordings you should keep in mind you’ll want a speedy way of doing dynamics control. IMO a good sampler should include a compressor/distortion for this reason.
FM synthesizers are chilly by nature, both volca and cycles.
Its mostly about clarity and how harmonic the sound is. FM is really good at those so it feels cold.
Try recording a Volca pad that you like into a daw, pitch it down and put a low pass filter on it.
If possible add some noise to it before the filter. If you like what you hear, model:samples can do that + be a drum machine.
Samples and Digitakt are a bit limited in memory capacity, 1gb of storage each, and thats the main reason why they have “drum” in their title. Otherwise they can be anything.
What this means is that you would have to store bulk of your samples on the pc, and only have the stuff that you are working with at the moment, on the device. (transfer from pc to device is easy)
Digitakt has more tools to interact with the sounds + can be a centre piece of whole setup, Samples has more immidiacy/ease of use to come up with ideas quicker + protability.
SP 404 mk2 rocks, but i think from these three devices youd need the most time spent with it for it to click.
There is also 1010music Blackbox, which i really like. Its not immidiate nor flashy, and arranging on it is like reading a book. Id say its the device that can create whole tracks by itself.
From what I experienced, I really liked the eletron workflow on the Model:cycles, so I would like to keep something close to it instead of having to learn a whole new interface.
I have watched a few digitakt videos and I am very impressed by what that machine can do. It looks like I could do full tracks with it and the nts-1. The model:samples seems simpler but a bit more limited (no resampling?).
But then I stumble upon this
And it is pretty inspiring…
So I guess now it is time to think before buying something.