Subs don't need to be matched to speakers in terms of sound, except in the case of having very small satellites that need a high crossover (some subs don't extend high enough). You don't have that problem though
However, you do need to be careful of getting a sub that has the right connections to integrate into your setup. With passive speakers and the Lepai amp, you either need
1) A sub that has speaker level inputs and outputs. You run the audio out from the Lepai to the sub, and then connect your speakers to the sub speaker outputs. This method has the advantage of allowing you to set the gain (volume) on the sub to match the speakers and then control the volume with the Lepai.
2) A sub with line in/line out pass through. Then you connect your source to the sub, and run the line out to the Lepai. With this method, you'll have to control the volume with your media source.
3) A sub with just line in inputs. Split the audio coming from your source and run it to both the sub and the speakers. With this method, you'll have to control the volume with your media source.
Also, subs should be matched to your usage. For instance, room size makes a difference in how much sub you need. Are you using it in a desktop computer setup only? Or are you looking for room filling bass? Is it mainly for music use, or movie watching, too? The latter benefits from <30hz bass output, whereas most music will be fine with a sub that doesn't extend as deep.
Finally, subwoofer availability and pricing varies wildly from country to country. Given that, I would find out what subs are available to you in your price range, and then go to AVS forums budget subwoofer discussion thread
. Share the models that you have found and see which one they recommend out of those.