Having only a 32x16 LED array to show data poses some limitations on the user interface.

The Nokia 3310 interface could be used as an example.  There are three functions in three buttons:

• C : Cancel = go back
• Middle : Select or Menu (which is actually also select)
• Up/Down arrow to choose items

To help with navigation, on the top right, the path in the tree is shown.  On the right, a line marker indicates the index of the menu item.

All in all that's very nice, but it forces you into a lot of key strokes.  Instead of a menu with several levels of hierarchy, the different functionalities will be brought out onto separate switches and rotary encoders.

Rotary encoder

The problem with a rotary encoder is that there's no way to go back to a higher level in the menu structure.  The workaround is to add a "Back" menu-item that points to a higher menu-level.

Filtered component list in Digikey for applicable rotary encoders with switch.  These are quite cheap, so they can be readily ordered on Digikey, no need to wait for AliExpress.

Another drawback of the encoder is the high switch actuation force.  For the Bourns PEC12R-series, is around 9N worst case.  That's about the weight of three soda cans (on planet earth).  This makes the rotary encoders unsuitable for horizontal actuation.  When you pushed the switch, you would turn over the clock, or it would start sliding over the surface if you wouldn't be holding it with your other hand.

The Bourns PEC12R series has a plastic shaft.  Rocking the shaft gently back and forth or left to right causes false contact switching.  The shaft also feels a bit flimsy.  Adafruit uses the PEC11-4215F-S24, which is now obsolete.  The PEC11R-4215F-S0024 is the new part number.  Presumably the metal shaft from the PEC11(R) series is more sturdy than the plastic shaft from the PEC12R.

Separate switches

Including the key cap(s), this is more expensive than a joystick if momentary switches are used. 

Using keyboard switches, it's another story.  There's a wide variety of push forces, key caps.

Because the original Cherry MX switches didn't accomodate for 3mm LEDs on a non-transparent key cap (which was what I had at that time), I opted to use SMD LEDs instead.  That wasn't a good option.  There's lots of light bleeding away on the sides.  Another problem is that only  the top half of the key cap is lit.  Using 3mm LEDs doesn't solve that issue.  3mm LEDs with a wide opening angle are needed.  Preferably the LEDs should also be high efficiency, as with charlieplexing, they might be driven with low duty cycles.

Keyboard switches are bigger than the ubiquitous 6x6mm momentary switch.  In this case, it's advantageous as it allows easier control.

Touch screen

A 6.2" or 6.4" touchscreen could be used (156 x 88 mm).  This costs $6.24.  Does a touchscreen have added value in this application that can justify the added cost? With a clever menu design, it can be very easy to use.

Joystick

This has all the necessary features:

• a button to select a menu item.
• up/down movement for selecting menu items in a list.
• left movement to go back to the parent level in the menu.

This single component can be used to implement the Nokia interface.  It might be strange somehow that the movement to the right has no function.

One handed operation.

The look might be odd with such a joystick pointing out on the front panel.

Navigation switch aka 5 way switch

The cheaper version of the joystick.  It uses switches instead of potmeters.  So there's no way of measuring how far the button has been pressed.

The key cap must be ordered separately.

1-Axis Thumb wheels

Very cheap, about $1.08 for 10 pcs.  According to Sparkfun, these parts are frequently used on portable MP3 players.

At least two of these would be needed.  For intuitive control, these would need to be mounted at 90 degree angles with respect to each other, so at the upper or lower corner of a device.

Even with two devices, these could still be operated by one hand.

They can also be bought from Digikey.

I ordered some of these buttons.   They're quite small and sometimes you push the middle button while wanting to move left or right.  When two of them need to be used, this no longer fulfills the single handed operation.

Scrollwheel

No suitable source found on AliExpress.  Available on Tindie.