I already have a 4 channel oscilloscope but it's quite old and I might have some money soon to upgrade with. The price for a 4 channel is almost 2-3x that of a 2 channel, but is the cost justified by the increased utility? I find I mostly use 2 channels on my scope currently, occasionally using a third but so far no use for all four. I'm dealing with serial protocols and video signals most of the time.
The times when I have needed a four channel scope, are few, but when I do there is no replacement for it. You mentioned serial protocols, using four channels can really help debug SPI communications, especially if the scope is fitted with a analyser to convert the SPI waveform into actual characters!
Having said that, buying a two channel scope, and then hiring a high end four channel with analysers (fft/spi and so on) might be a worthy alternative.
The saving you make up front, can go towards the hire cost of when you actually need it! Might be worth investigating the hire cost upfront so you know what you might be in for.
Personally I use 4 channels all the time for analog work, but if you're not doing something that involves multiple stage audio filters or something of that nature it may be overkill.
As long as you can verify signal integrity you shouldn't need very many analog channels for what your describing. You're better off having a scope with a higher bandwidth so you can see EMI issues than you are a 4-channel scope. For instance in your application I would get a 2 channel 500 MHz scope over a 4-channel 100 MHz scope. I would make sure the scope has good math and FFT functions.
Also consider any differential measurement issues, unless your scope support differential probes your 2-channel scope can only measure a single signal differentially.
The only caveat I would add to the number of channels is if you're doing design for mass production. The first time you run into some weird intermittent error that only occurs on some boards you're going to want to be able to scope as many signals as possible in the analog domain while you try to induce the error. This is much more common than it sounds.
For digital work, as long as you can verify signal integrity issues I don't find having the scope be able to decode serial data to be all that important. Using a USB-to-serial converter for the appropriate serial bus type I find much easier to work with. The amount of data I can store on my computer and how quickly I can navigate it with a mouse/keyboard massively surpasses every scope I've ever worked with, unless you're talking very high speed, like PCI-express or something.
Also being able to act as a master on an I2C/SPI bus is very useful for testing slave functionality. I can write up a Python script to test all functions of a slave device much much faster than I could trying to do that from the board's true master.
If you're working with higher speeds or parallel buses, a logic analyzer may be very useful. The one I work with a lot that doesn't operate within the USB<->serial realm well is I²S, and I don't bother with the logic analyzer; I check the signal integrity with a scope then feed it through a little converter board I made that converts I²S <-> S/PDIF and feed it right into my computer to analyze in MATLAB.
Some scopes will do video triggering on NTSC/PAL/HDMI which you may find useful.
I have no idea what your budget is. The scope I use most is a Tektronix MSO3014 which is a 4 analog + 16 digital @ 100 MHz scope, which I find takes care of 95% of what I need, only failing to meet my needs when the bandwidth isn't high enough. But at ~$8,000 it may not be what you're after.
My view is that two channels is usually enough for analog usage, but four channels is not enough for digital use. I have an Agilent scope with two analog channels and 16 digital channels. As long as you don't need to probe very high frequency signals an oscilloscope like that should not be too expensive.
We have 2 and 4 channel scopes round the lab, and sometimes 4 channel is a lifesaver... however, these days we are just as likely to break out the BusPirate or Open Logic Analyser from Dangerous Prototypes when debugging digital stuff, especially comms protocols. There's some good scripting and capture capabilities that even a $1000+ (or $5000+) scope won't have.
Total cost for both devices plus some nice colourful hookup leads will be a lot less than the extra you'd pay for your 4-channel scope, and between them they extend your capabilities further than an extra 2 channels.
2 channels analogue is fine, then get a USB logic analyser for serial protocols (I like the Saleae ones)