The SID machine is an emulation of the C64 MOS chip named SID.
The first Elektron product was the Sidstation, a synth based on the Sid chip, that used the real chip, no emulation.

The Sid machine acts as a single sid oscillator with sync/ ring with some added feaures like a modulator that can use its own frequency or the previous channel freq (a sort of  FM between two tracks).
This machine is one of the easiest to use and at the same time it is really effective and can produce a vast array of sounds , not only computer like sounds.

HOW TO CREATE A CLASSIC C64 ARP

First you have to choose if you like a more percussive or melodic arpeggio.
For a percussive one I think the square wave is recommended , cuts harder…
The ahdr must be set for a quick and blieep sound.
Use the hold to sustain the note (value 2) and a low value for decay and release, so the sound will buzz fast and with a typical computer behaviour.
Use the pulse wave with PW (64) and PWAD (64) , then turn on the ARP (press FUNCTION+ARP) and set the SPD (3) , MODE (sid), PLAY (cycl) and RNGE(3oct).
Pressing a single key the arp does not activate, while pressing more than one key will activate the arp in a sid-like way , try a 3 note chord!

Another interesting sound for arpeggio is switching on the MOD to R+S (with all the previous settings) and add a little of movement modulating the MFREQ ith an LFO.
Go into the LFO1 page set PAGE (SYNTH), DEST (MFREQ)and DPTH (60).
Done!

To add a little bit of “digital imperfection” turn the SRR to 64 in the  EFFECTS page.