Rant mode = on.....
I know Dave has a whole video about analog scopes, and everyone keeps suggesting them to people, but seriously? For someone doing embedded systems design, an analog scope's main purpose is to look cool in your lab and collect dust. The main strength of an analog scope, especially the old ones people sell for under 100 USD, is to look at nice repetitive analog signals. They answer questions like "how much does that cheap opamp distort the sine wave and what is approximately the amplitude". Or, "What is the time constant on that filter if I run it with a square wave".
If you are doing basic embedded digital design, you need a scope with single shot memory captures that you can zoom in on. That is the #1 thing you will use the most on a scope. Stuff like looking at data bursts, signal glitches, and voltage levels during events. None of that is repetitive in the nature that makes them easy to measure on an analog scope. And as a bonus, the DSO will do all of the basic analog scoping with the ability to accurately measure and report all the values like amplitude, frequency, duty cycle and stuff like that right on the screen with way more accuracy than counting boxes. The traces will be different colors so you can actually tell them apart on the screen too. 100mhz is fine, but as always, buy as much bandwidth as you can afford. Also don't go too old on used DSOs. DSO technology exploded recently, especially in the low end. Even with 10 year old tech, it's like model-T vs Ferrari.
You probably can't get away with just having a logic analyzer since you will need to see how circuits effect analog voltages, but having both is the ticket here. Just the scope should be good enough to start and add a logic analyzer later. Or get one you can later upgrade with the LA option.
I'm going to get flamed for this, but I'm going to say it anyway. Despite what people might tell you, there is no real good reason to own an analog scope for general purpose use these days if you can get your hands on a decent DSO. If you need one of the specific reasons an analog scope is better, you already have a nice one right next to your nice DSO on the bench. You don't see Dave using that analog hameg on a daily basis unless he's looking at an XY screen saver. There is a reason for that. Save the money and put it towards a DSO. Pick up the analog scope later when you want to make your lab look cooler. If you are considering spending 600 bucks, you can probably afford the rigol2000 series. You probably won't regret it either from what I've been hearing.
On a separate note, if you are just starting out in the analog world and want to see how various component configurations effect circuits and such, I've found the best way to do that is in a simulator. Pspice is pretty easy to use as they go. You don't have to have a huge stock of components and equipment and you can try any value you want just by changing some text. I know it's kind of cheating, but you should have a solid intuition of how circuits work and this is the fastest way to experiment. Plus you probably won't let the smoke out of spice.
Rant mode = off... (sorry)