I'm getting back into basic electronics with an Arduino after many years away from the hobby, and I've forgotten a lot of my knowledge.
One thing I'm finding is that I really need to get an oscilloscope to assist in designing filtering circuits to give me smooth output from PWM.
I'm not after anything fancy and my budget it small, so what sort of things are on a an oscilloscope must have list?
Digital vs. Analog: I've a preference for digital, because I'm often looking for transient stuff, and I like being able to stop on a trigger and really look at the signal. This is somewhat dependent on the work you do, but I think it's mostly an artifact of what you are used to. I came up working with digital scopes (and scope/logic analyzer hybrids), so that's what I like.
Bandwidth: Just make sure it's high enough for what you want to look at (I do old arcade gear, which tops out in the < 20 Mhz range, so I don't need a lot of bandwidth). Remember that this is the ANALOG bandwidth - not the sampling rate of a digital scope.
Sampling rate: Digital scopes only, of course, but with digital scopes remember that the sampling rate is NOT inherently related to the bandwidth. It's entirely possible to have a scope with a high bandwidth, but a sampling rate barely able to meet Nyquist on that bandwidth.
Memory depth: Again, digital scope only, but important. Especially important is to look for shady specs like only being able to sample at full rate with a part of the memory buffer. This trick is kind of common and quite annoying, because it makes comparing the sampling rates of different scopes quite difficult.
Specialty items: There are a lot of 'USB scope' things out there these days. BE CAREFUL! Especially if they say 'unlimited buffer', you want to look closely - those scopes turn out to be sample rate limited to however fast the USB bus is on your computer. In an optimal situation they should be able to meet their stated sample rate, but if something (driver issue, competing device, whatever) slows your computer's USB bus down, then your sample rate can drop. On the other hand, they are usually quite cheap.
If you want a good scope for not a lot of money, pick up just about any analog scope from ebay. I've had a Beckman Industrial 9022 and never found it lacking for hobby use. It's a 20 MHz scope, and there are few things that require anything faster. The fastest thing I have on my desk is a micocontroller clock, but even if for some odd reason I wanted to run my AVR at maximum speed and I wanted to scope the clock, at 16 MHz it's still visible. Maybe not super sharp, but fully resolved at least. Unless you plan to build any RF circuits soon, I doubt speed will be a concern.
Despite the tech gadget factor of a digital scope, there are some things that show up better on an analog scope. The cheap digital scopes I've had the displeasure of using have the problem that they can't update the display very fast, while an analog scope updates the display instantly each time it triggers. This is great when you are looking at noise superimposed on another signal; with an analog scope you can see the trace brightest at the most frequent values, and dimmer regions of the trace for the rarer excursions. On a digital scope all you get is a sharp trace that wobbles, to whatever the noise happens to be each time the display updates. I'm sure there are digital scopes that address these shortcomings, but they will be out of your price range.
You might miss the storage capabilities that every digital scope has, but I don't. For things I need to store, a logic analyzer is usually the right tool, and for the other times, dimming the lights, turning up the brightness, and using the single trigger mode works well enough usually. Analog storage scopes do exist; maybe you can find one for a good price.
In all, I think what you lose in high-tech gadgetry you will gain in quality construction and robust engineering. New, inexpensive digital scopes are made in China and will break in a couple years. A used analog scope for the same price was made in the same country that designed it with parts made to last 200 years.
For the uses you mentioned, at least 25MHz and at least 500Msps. But of course the more, the better. Since oscilloscope manufactures arrange their product lines along a price range, the other parameters will have correspondingly adequate values, usually. Also I'm biased against both pocket and USB models, the former because they are "cheap" (!) and USB because they are more limited and less practical. Sparkfun has a model with quite better features, but at a reasonable price for them.
For your given use, just buy anything of a known make 2nd-hand for peanuts, low-speed (<50MHz) analogue scopes go for a pittance these days. You don't need fast or fancy. Anything with a Tektronix badge will do. Used but known stuff is preferable to cheap new chinese stuff as you know there'll be parts & service out there if you need it.
DSO's are nice but you have to remember they will lie to you as the signal is by definition always processed.
The Seeed studio DSO-Quad / DSO-nano are nice open-source pocket scopes and perform well enough for whatever you want (and can also play tetris), but can be fiddly and the screen is of course quite small. For the money I'd rather have a cheap used analogue or CRT-DSO scope with knobs and buttons as my main or only scope.
