What's the best cable/internet packages available?

Lately we've been having problems with our internet. It's too slow and our devices always have trouble connecting to it. My laptop, phone and xbox, My sisters laptop and iphone never seem to want to connect.

Right now we have Time Warner cable for our internet. My parents pay about $44 something a month for it so I'd say that we have either their "Turbo" or "Standard" package which is supposedly giving us 15-20mbs download speed but after checking my speed at Speedtest.net, it says we have 3.23mbs. My guess is Time Warner is over charging us? I don't know.

Anyway, I'm trying to help my parents find a better deal. We don't watch that much TV, other than AMC, TBS, and Comedy Central. I'd like something that carries FX also.

So what are some good packages that emphasize internet, but not so much television?

Also, could my internet problem be because of our router/modem? I'm not that tech savvy so I don't know, but our hardware here is pretty old.

Uverse is the best product i would probably recommend you to get. They have speed up 45mpb for HSI and tv and for wireless and phone.