High resolution angular position (~0.5 degree) measurement
There are many ways to measure angular displacement. I have had success with both variable capacitance (using the sub-pF changes to control a VCO, and then counting the resulting frequency) and magnet+linear Hall sensor (crossed axis, so the Hall output swings above and below the zero that occurs when a bar magnet is pointed straight at it).

However, as it tends to be the best in terms of resolution, accuracy, stability, absence of force back on the experiment, the go-to method that most researchers use is the laser+mirror+sensor setup.

Maybe it's worth persevering with a little more. Your comment 


  I am having a lot of trouble with reading the reflected laser and I have tried (and failed) at getting a proper data readout from data sensors.  


suggests that it's worth concentrating on the sensor side. 

The classic laser beam sensor consists of just two photodiodes, and is only intended to detect a reference position, when the intensity of light on the two diodes is equal. 

For small deviations from this reference position, you get a monotonic, and generally fairly linear unbalance in the two outputs. 

It's possible to extend the array of photodiodes in an arc, and using a multiplexer, read the array to find which pair the beam is between, and then using the ratio between those two, estimate an interpolated position. As you don't need high angular resolution, it might be worth increasing the beam size so that it illuminates more than two diodes. This will allow you to make a more linear interpolation of spot position.

If you don't grok photodiodes, then you could always use LDRs (light dependent resistors), and read the illumination as resistance. They're not as fast, linear, stable or well matched as photodiodes, but I find them a bit more 'friendly'.

You can run into problems if you use a conventional (back-silvered) mirror. It's worth using a 'first surface' mirror, they're fairly inexpensive in small sizes.