What kind of reciever do I need for my turntable and speakers?

First, on your turntable that has speakers, is there a pair of red and white RCA connectors on the back? If so, you can hook it up to an amp as long as the amp is set up with a phono input. If the amp doesn't have a phono input it will not work. Phono RCA inputs are different than the RCA inputs for CD, DVD, Xbox and so on. Phone outputs use a much weaker power level, and require an amp to amplify the phono single much more.

That doesn't look like a turntable. Turntables don't have built in amplifiers, record players do. I don't see how you can use it with another receiver; you can't run an amp into an amp. That receiver looks fine, but you may have to buy a real turntable. Yamaha stuff is pretty good.

First off, the system you have does not have any audio pre out for connect another power amplifier to it. Those all in one system are not flexible for upgrading or connect anything to it or out. The receiver your are looking at is a multi channel receiver for home theater. You are better off buying a stereo receiver. If you plan to use it with your tv then it is ok along with your 360. I would rather you look ata Pioneer or an Onkyo receiver, they are the best entry receiver in the market. Then just pick up a turn table to connect to the receiver. If you do you have to make sure that it has a phone (turntable) input on the receiver. Your system is too old and outdated. Hope this will help you out.

Well honestly your going to have to be very careful choosing speakers to work with your system, otherwise you could damage the receiver portion of your system. First you dont want any Sony or Bose speakers not only are they terrible sounding, there are much better choices. Also to be honest just buying new speakers may not solve the problem as it could also be a issue with the turntable and system. This looks like a very low end system and just buying new speakers may not be the right solution. To assure you don't damage your receiver, you need to choose speakers that are a easy 8ohm load, meaning so the impedance of the speakers stay around 8ohms do not go below 6 ohms or higher than 12 ohms. You also want a pair of speakers that are fairly efficient (meaning they don't need allot of power to drive them to decent sound levels) Stay with a speaker manufacture that all they do is make speakers, as this also assures this is what they specialize in and built there reputation on making just high quality speakers. So speakers that have a nominal 8ohm impedance, are 92db 1 watt 1 meter efficiency or higher. Kevin 40 years high end audio video specialist