I agree with "astrallite." 2.1 is good for music, 5.1 is good for games.
If you are just beginning, you want to start with simple 2.0 or 2.1 speakers. A 5.1 surround sound speaker system sounds great, but has a lot of problems.
1. They are expensive. Good 5.1 speakers cost at least $250.
2. There are a lot of wires and you will probably be moving the rear surround speakers every time you want to watch a movie or play a game.
3. You will need some way to place the rear speakers behind you at ear level (about 4 feet off the ground). You can buy stands for about $100 or find chairs, tables, boxes or other items sitting around your house. You can mount the satellites on the wall but that requires buying mounting brackets and using a hammer, drill and screw driver. Not to mention putting holes in the walls.
I do not recommend wireless speakers. Some of them produce a hissing noise because of the interference from other wireless devices like cordless phones. Avoid speakers designed for laptops. They do not produce good sound for games and music.
Here are a few suggestions:
M-Audio Studiophile AV40 ($150) - I own these and they sound great with music, movies and games. But they are big, heavy and expensive for 2.0 speakers.
http
/www.sweetwater.com/store/detail/AV40/
M-Audio Studiophile AV30 ($100) - Same as AV40 but with 3 inch woofers instead of 4 inches.
http/www.bestbuy.com/site/M-Audio+-+Studiophile+3%22+Bookshelf+Speakers+%28Pair%29/8452747.p?id=1183767507654&skuId=8452747&st=studiophile&cp=1&lp=2
Altec Lansing VS4121blk ($68) - A friend of mine has used these for about 4 years. He mostly plays music on them, he's not a gamer.
http
/www.officedepot.com/a/products/591350/Altec-Lansing-VS4121blk-3-Piece-Speaker/
Speakers at Best Buy - Do not buy Bose, Insignia, HP, Cyber Acoustics, Sony, GE or Axis. Spend at least $40.
http/www.bestbuy.com/site/Computer-Speakers-Headsets/Computer-Speakers/abcat0515039.c?id=abcat0515039
Creative GigaWorks T20 ($100)
Creative GigaWorks T40 ($150)
Klipsch ProMedia 2.1 ($155)
Logitech X-540 ($100) - Cheap 5.1 surround
Logtiech Z523 ($90)
Logitech Z-2300 ($170)
Logitech Z-5500 ($400) - This is way out of your price range, but it's one of the best 5.1 speakers for computers.
http/www.newegg.com/Product/Product.aspx?Item=N82E16836121120&Tpk=logitech%20z-5500
Also, any speaker system with a subwoofer (larger than 5 inches) will annoy your neighbors or family members. The low frequency bass travels through walls and floors. You may want to buy a headset/headphones for playing games at night (when everyone else is sleeping). I like the over-the-ear designs with a microphone. They have padding around the ears and top of the head. I do not recommend buying a headset with a USB port. This overrides your sound card and sometimes causes hardware/software conflicts. Also, do not buy earbuds; those little headphones that fit inside your ear canal and are designed for MP3 players. They are not good for games that have explosions and gunfire.
Plantronics GameCom 777 ($50)
http/www.bestbuy.com/site/Plantronics+-+GameCom+377+Over-the-Head+Stereo+Headset/8978403.p?id=1218004379967&skuId=8978403
Sennheiser, Creative and Logitech all make good headsets.