Computer Speakers

Of course turning the bass down will also make the volume appear to go down.

This is due to the basic physics of sound.

Put simply a soundwave at low frequency is longer than one at high frequency, and thus consumes more energy, and as what you put in must also come out imparts more volume to the mix.

I would suggest, therefore that it is not the speakers which are at fault, but probably the amplifier driving them?

You can't expect to get good quality sound from an amplifier which only has control over bass. The reason the sound becomes muddier as you turn up the bass is because as the bass drivers consume more energy, the crossovers in the amplifier begin to limit the high frequencies in order to accommodate the bass.

If you are looking for better sound quality then you would be better off using the line out from your computer sound card to drive a standalone amplifier driving a graphic equaliser and stereo speakers. But be prepared for a hefty knock to your wallet.

I'd suggest, though, that it would be possible to get much better result simply with better computer speakers. $30 is squarely in the "toy" range. Expect complete junk at that price raange. But for around $100 you can expect much better results by default even without fancy separate component amp/eq/speaker systemsthat would generally take up much more space, draw much more power, require a tangle of cables, etc. i use a pair of Roland powered speakers that are unfortunately no longer made, but there are similarly-spec'ed systems from JBL and other audio companies that would very likely make you perfectly happy.

Anything will sound better on a laptop! ;-)
Have you considered headphones?

Still, if you are set on getting speakers, here's my suggestion:
You will need something with a powered subwoofer. That is, the setup needs to be plugged into an electrical outlet - to power the amp. 'Total watts' roughly translates into 'loudness'. Also, many computer speaker systems have a remote master volume control, along with a separate bass volume control (for the subwoofer).

What I use:
I am primarily a fretted, stringed instrument player (non singer) who recently acquired a Yamaha keyboard, which has many of the great musical instrument sound samples that are available nowadays - horns, strings, grand piano, etc. Needless to say, the keyboard's onboard speakers lack quality sound (therefore, I mostly use headphones). However, I did buy the Cyber Acoustics CA-3602 speakers to play indoors at a family gathering. Though they are touted as 'computer speakers', they sounded clearer than my 50 watt Peavy keyboard amp! (I am not affiliated with Cyber Acoustics... lol). The speakers also work well on my desktop computer. They are rated at 30 watts. If you're not in a hurry, you can wait for a sale. I got mine for half price.
I don't know what you bought at Radio Shack. I hope they weren't these.... :-)

Also, speakers don't have to be "compatible with Musescore". They should play any audio your laptop outputs - music, movies. There is one thing, though, that might affect Musescore's playback - more noticeably with a decent speaker setup - and that is the soundfont you choose in Musescore. See: http://musescore.org/en/handbook/soundfont

With regards to "lightly shaking" the walls - it all comes down to energy, i.e. total watts. Deep bass and/or percussion at sufficient volume can rattle stuff - not necessarily the throw pillow on the sofa, but more likely the empty ceramic coffee mug sitting on the edge of the glass tabletop. I'm sure you've heard a car driving by with an over-the-top subwoofer setup: the low frequency bass/percussion heralds its approach.

Since I have lots of time, let me ramble on...

It also depends on the type of music you want to reproduce.
To illustrate:
After the introduction of CD's and digital media, music producers started adding lower frequencies, and higher volumes, to recordings. Gone was the inherent physical limitation of a phonograph needle tracking a narrow groove on a record in order to generate an analog signal. Sound waves could be reproduced digitally using bits and sampling rates. Some say digital signal processing has created a "loudness war". See: http://en.wikipedia.org/wiki/Loudness_war

One only has to look at, for instance, the dance music (which supplanted disco) that came out circa the early 90's to notice this emphasis on driving bass and low frequencies, not to mention the rise of the subwoofer! Anyone remember the #3 hit from 1991 (USA Billboard Hot 100) - "Gonna Make You Sweat (Everybody Dance Now)" by C+C Music Factory?

Or how about #6 - "Unbelievable" by EMF?
Compare that last one to #15 from the same year (1991) - "From a Distance" by Bette Midler.
(OK, I will. See the attachment ('Loudness.JPG') which shows a waveform comparison of the two songs.)

So...
100 watts and greater will shake stuff, but it will cost more than a 30 watt setup.
Depending on your tastes, 30 watts may be good enough. Anything - even headphones - would probably be an improvement over laptop speakers.

OK ... Time's up! Regards...