You probably need something capable of 100 MHz, or, at an absolute minimum, 80 MHz if you plan to work with microcontrollers that operate at 12 MHz or more.

If you're going to observe signals on a microcontroller, you need an analog oscilloscope with 2 channels + external and internal trigger, secondary (delayed sweep) timebase, sensitivity down to, say 5 mV, ... look at the specifications for a TEKTRONIX 465 (no longer made), or, its equivalent in a digital sampling oscilloscope, which means you probably want about a 500 MHz sample rate. There are some that manage a reasonable presentation and some accuracy (meaning repeatability) and precision (meaning resolution with respect to real values) with lower sampling rates, but the results are "muddied" by the repetitive sampling.

Look around for specifications of older used oscilloscopes from major manufacturers. That will give you an idea of features available on those instruments. The features I mentioned are pretty common on analog 'scopes. I gave away my first 'scope, which was a TEKTRONIX 465, about ten years ago, after having it since it was new. I now "get by" with a TEKTRONIX 475A (250 MHz) with the DM44 multimeter built in and a somewhat fancier 4-channel TEKTRONIX 2467 (400 MHz), which I bought specifically for investigating metastability in high-speed (>200 MHz) circuits because it has a very handy photomultiplier on its display, which allows me to see events that occur only about every 50 million sweeps or so.

Several of my clients have much newer instruments that sample in the tens of GHz. I personally don't like digitally controlled test equipment, which, BTW, that 2467 is, as are those digital 'scopes. The 475A is nearly identical to the 465, aside from its higher bandwidth, and that suits my hands very well, no longer requiring that I look at the knobs at all. Keep in mind that you have to have probes that have adequate bandwidth to match or exceed the 'scope, AND all the attachments/accessories for those probes, as you'll never get them if they're not included with the probes.

RE