I generally use RS part 488-2610 (24VDC coil, but other coil voltages are available), along with the holder 803-376

You'll likely get equivalents far cheaper on AliExpress, but there are lots more types depending on what you're doing.
I find that DPDT a useful size for what I tend to do, so keep a few in my stock, but have also used much smaller versions, along with bigger versions.
Using DIN rail makes cabinets far neater, and makes later changes a bit easier than just a jumble of wires going directly between things.

If you need something for bigger loads, a contactor usually makes more sense, or a SSR (Solid State Relay), however a caution is SSR relays can fail short circuit.
For something like controlling the power to a router on a homemade machine, I'd probably go for an SSR, as they can be had quite cheap, and the risk of failure isn't that high, and should the worst happen, the rest of the machine should still stop.
However on an industrial machine if I wasn't using a VFD controlled spindle, and need power disconnected reliably, I'd use a contactor, as the chances of one welding completely shut is very slim.

For example my ongoing big mill retrofit, power to the servo drives is handled via two contactors (each powered up with a 1 second time delay to reduce the power up surge).

Key thing you need to work out is how big the load is, and what power you have available to power the relay coil.
An Arduino will only allow loads of around 10mA (IIRC they can handle 20mA, but 10mA gives a good safety margin), so you'll likely need to use interface/signal relays to power bigger relays.

You'll also probably want to use differential line drivers to interface the stepper drivers, and some form of buffer/opto-isolator inputs to an Arduino.
The low voltage of the Arduino means they can be prone to noise and false triggers, which can cause a whole world of pain if your shielding and wiring isn't perfect.

I'd strongly recommend you make all the control wiring 24VDC, then have suitable interfaces to the arduino, as it will make things much more noise resistance.
The interfaces can be done pretty easily on strip board with suitable chips, provided you don't mind a bit soldering.