I'm torn on this... on the one hand I feel if you can get your hands on a used scope at a decent price you will have a fairly usable piece of test gear that will do what you want now and give you a tool to learn on.
if you are going to measure power supply noise, its helpful to get one of the scopes that can go down to 500uv, and at least 20mhz of bandwidth. there is a thread on what scopes can do that.
https://www.eevblog.com/forum/beginners/500uvdiv-oscilloscopes/ buying a used CRT based scope is really a good option. Especially if you are on a budget.
on the other hand If you are willing to put some more money into this, at 499 usd Siglent SDS1104X-E 4-Ch 100MHz and at 379 usd Siglent SDS1202X-E 2-Ch 200MHz are stand-alone digital scopes but can also be hooked to your computer that offers good value for the money and are my current personal prefreces
both of those scopes offer some very advanced features which you might not appreciate now but will if you continue and grow in your knowledge you will quickly make use of. for now, one of the important features is it has true 500 μV / div sensitivity (not software enhanced which is important when looking at noise)
These scopes will grow with you with most needed features already in there out of the box and the ability to add more if needed. You get one of those, you will likely not be wanting for a different scope for a long time.
i used to be a BIG advocate of learning oscilloscopes with a CRT based scope because it illustrates exactly what is going on with the controls on your digital scope, it helps with the understanding of it. but in this age of smartphones, starting with a digital scope like the siglent is not a bad place to start as it can perform many functions that you would traditionally need additional gear for, voltage meter, frequency counter, rudimentary spectrum analysis, protocol decoding of digital data. and you can add things like signal generation for sweep functions and various waveform generation, and the ability to add on logic analyzer functionality. This makes for a very compact workspace
for your use ... lets say you look at the power supply and you see noise. and you want to dig deeper and see what frequencies make up that nose. you can pass that thought the scopes build in FFT and see the frequencies and amplitudes that make up that noise. pretty sweet. you can't do that on an old CRT based scope!
i think your smart taking a moment and researching some more ... and i'm sure some of the terminologies is new for you, and that's fine. It gives you some things to research

Most of us have bought equipment/tools that we outgrow almost immediately or overspending on things we just don't need..
hope our experiences/insights help you make a good choice for you.. but start someplace, it is better than not starting at all

have fun!