Hi Ben,
Whilst the sample rate and bandwidth of the device may be sufficient. A couple of things you have to take into account:
How long you wish to look at that data for, the 2203 memory is 8KS for one channel so if you were to look at a 25kHz signal you may need to sample at 250kS/s. As such you would use a time base of 2ms/division giving you 20ms of data. The more memory you have on a device the longer you can sample at higher rates.
Second thing is the vertical resolution, the device is 8 bits and as such in your +/-5V range, you will have 256 steps. If you used a 12 bit device you would get 4096 points.
So it depends really on what you are looking for. If the memory and resolution are not a major factor then the 2203 should be fine. If not then you can go for something like the 3224. Which has 512kS and is 12 bits.
http://www.picotech.com/pc-scope.html
Kind regards