Amplifiers have less impact on sound than speakers, but they do affect sound quality, as well as how loud your speakers can play. If you're buying more expensive speakers, it usually helps to buy a more expensive amp. Again, specs don't help much here, but the bigger and heavier an amp, the more power it can produce.
Start by looking at the $99/£/$144 (about AU$127) Dayton Audio DTA–120. It will push these speakers to respectable volumes, and do so without obvious flaws.
Want to take a step up? The $219 (about £142/AU$279) Emotiva mini-X a–100 will give you more power than you need.
Or, start looking at full-fledged receivers, which give you a remote, more connectivity and features, and, in the case of home theater receivers, video switching and the option to add more speakers for surround sound. Check out the $299 (about £194/AU$381) Denon AVR-S500BT - a great value for stereo or home theater at a street price of $249.
Space-saving sound bars
Don't have the space for two speakers? Sound bars fit below or in front of your TV. They don't sound as convincing as true stereo speakers, but they'll easily beat out what's built into your TV.
If you have your TV on a stand, look at the $299/£194/AU$381 ZVOX Z-Base 420, available for street prices around $199. It acts as a pedestal for your TV, allowing it to take up more space. The extra space means there's a bigger speaker cabinet and bigger drivers for better sound.
Also worth considering is the $249 (about £162/AU$318) Vizio S4221w-C4, which includes a separate subwoofer (making the sound bar small enough to fit in front of your TV), and a larger feature set.
Finally, the $449 (about £290/AU$573) Pioneer SP-SB23W (with a $339 US street price) and $349 (about £226/AU$445) Pioneer SP-SB03 (occasionally a steal at a $174 US street price) offer the same Andrew Jones design that makes the SP-BS22-LR such a killer set of speakers. The SP-SB03 comes in a pedestal form factor, while the SP-SB23W is a traditional sound bar with a separate subwoofer.
Finding the source
Now that you have what you need to make some noise, you need some noise to make. Fortunately, this is the easy part. Computers, TVs, tablets, set top boxes, and smart phones can form the core of a high-quality system - just hook them up to your speakers or amp.
One thing to consider, though, is cutting the aux cord - you probably don't want to be separated from your phone anyway. Bluetooth audio receivers make for a convenient upgrade. As long as they transmit using the newer aptX, MP3, or AAC codecs, they sound great - just avoid models that rely on the old SBC codec.
The $39 (about £25/AU$51) Avantree Roxa handily packs its everything in the form of an AC adapter to reduce clutter. But if you really want to hear your music at its best, take a look at the $150/£90 (about AU$191) Arcam miniBlink, which has a high-quality digital-to-analog converter (DAC) for optimal sound quality.
Odds are, you spend a lot of time listening to speakers in some form or another. It doesn't take much money to make that experience much more pleasant. If you haven't thought about an audio upgrade before, now you have no excuse.