What are amplified speakers? Are they good?
Amplified speakers are good, yes. Amplified speakers are speakers that have their own power connection, be it from batteries or an AC outlet. This type is opposite to passive speakers, which are powered by your computer's sound card. Amplified speakers are capable of much more power and volume, and are the only viable choice if you want a speaker set with a subwoofer or more than two speakers altogether (for surround purposes). Passive speakers are usually cheap and small, so they suit some people's computer needs. Still, for sound to let you really enjoy gaming and multimedia, you certainly want your speakers to be amplified speakers.
Since your use is limited to the desktop computer, there are many many different brands of amplified speakers which will do the job. Some look very attractive, some are just plane jane. See if you can get a demo. Most of these are suitable for listening to music at the lower levels so you can work at the same time. They are usually value for money.
you need amplified speakers unless you have an amp. You will be able to use speakers without an amp, but you wont get much sound out of it.