I was wondering if someone here could point me to as few Arduino projects the would assist me in learning to use my oscilloscope.
I've used the arduino to view a, "square, sine and sawtooth wave." I've also done serial decoding. My scope is the Siglent SDS1202X-E. TIA
Many many oscilloscope videos on YouTube 
For the Arduino, go through all the examples in the IDE.
Most digital signals are non-repetitive in the short term so depending on what you're looking at, they can look like "garbage", especially after the 1st pulse. It can be helpful as a rough-check to see if a line is switching high and low, or stuck/shorted high or low, and it can be quicker than a meter if you just want to check the high/low state of something (if your 'scope is set-up and running).
Sometimes, you'll see some weird half-step signals if two data-lines or two address lines are shorted together, but with the Arduino all of the "regular" data & address lines are inside the chip anyway.
A 'scope can also be helpful if you're looking for noise on a DC signal or power supply, etc.
Of course, if you have some specific timing that needs to be measured or checked, the 'scope can be the perfect tool.
...I use a 'scope a lot at work (it's required for some of the tests I do) but so-far I can't justify having one at home. Sometimes I do "lust" for one. On one or two occasions I've brought something into work to check with the 'scope. Once I had a shorted Arduino output pin (maybe shorted to ground but I don't remember) and that would have been easier to find if I had one at home.
Find some analog sensors to interface to the Arduino, and also probe with the 'scope? Microphone, accelerometer, photodiode (point a TV remote control at it for instance).
With a dual channel 'scope you can look at clock and data pins of I2C bus, or SPI bus, seeing how the
relate to each other.
Again with dual-channel a quadrature encoder can be observed.
I would go on line there are a lot of tutorials. Also you need to determine which world you are working in, analog, digital or both. Displaying the wave is simple, interpreting it is where the skill is. I have both scopes and logic analyzers. In the Arduino world I use the Saleae logic analyzer, it does a great job and is fantastic for communication protocols. You need to understand what probe capacitance is and how it will change your circuit.
Logic analyzers are a bit of a pain to use, normally its 'scope first to look for obvious problems. Then you might have to connect up all the many probes of the L.A. and try to capture the miscreant events. For simple Arduino stuff there is seldom need for this, a dual-channel 'scope is often enough (but 4 channels is great), especially as modern 'scopes capture events to USB sticks so you can compare multiple waveforms offline too.
Logic analyzers cannot diagnose any analog issues like ground-bounce, bad logic levels or runt-pulses
either, they only come into their own with the sort of complex digital systems that are now implemented with surface mount chips (try connecting your 16 LA probes to a TSSOP package!).
In the old days these clips plus a LA were very handy: https://uk.farnell.com/3m/923690-16/test-clip-dil-16way/dp/178272 - no longer manufactured.
In short 'scope will get you a long way, L.A. is much less likely to be needed, especially with microcontrollers where the most complex bus is SPI.
There is one cravat to the logic analyzer you have to learn how to use them. My cheep logic analyzer works at well over 20Mhz, My good one is in the GHz range, the same as my scope. Normally I only connect 1 or two wires, depending on what I want to see. If it is a serial stream it will tell me what type and the data shown. Oh yes I can capture date for minutes, my scope will not do that.