Your approach is a tad wrong. You won't ever know if you need to use it - how would you? You're not an oracle. What you do is you use it first, and only then you have proof that everything is peachy. My bet is that you have very poor idea as to how your circuits really perform. Just because it "works" doesn't mean it's anywhere near being properly engineered. Just look at transition times on modern micro controllers and on the discrete logic chips that you're using. If your scope won't let you see those transition times, it means you have no idea what effect all those transitions have on your circuit as a whole. For all I know your power supply is sagging every time a GPIO pin is switching, and your circuit works just because you got lucky, but it's much closer to not-working. There's a lot of analog design know-how that's needed to properly design "digital-only" electronics.
It took me 15 years to be at a point where I claim I know a bit, and I still consider myself quite dumb when it comes to analog. Well, at least I've got a multi-kW piece of power electronics to pass emissions on the first try, with a whole bunch of cables attached to it - that's kinda hard. It only happened because I was quite conservative in everything, and paid attention to a whole lot of details that don't matter at all in whether "it works". Now of course emissions and susceptibility often go hand-in-hand, so if your circuits ring all over the place, it may also mean that they'll pick up things you don't want them to pick up once someone places a cellphone nearby
Yes, I know that if you're on a tight budget, you simply have no option of getting more advanced test gear. If you're in the U.S., I suggest you keep good eye on eBay for used brand-name equipment. Sometimes you can get absolutely exceptional deals. A lot of older analog-style test gear is quite repairable, with free (or very affordable) service manuals available. There's a few exceptional all-transistor, no-custom-IC Tektronix and HP oscilloscopes out there, that go at least to 100MHz. They'd be still considered a baseline kind of an instrument. If you've got room for it, something is to be said for Tek 7603 mainframe. There are mailing lists / discussion groups for every brand of test gear out there, often with folks who used to design the very instruments you now get on the cheap.