Mark:
It sounds like you are very new to the world of turntables and stereo playback in general so let me go back to basics to describe the various devices that are needed to play back records.
Starting with the record:
The record is run on turntable. That turns at a constant speed, 33 1/3 rpm for lp's. The quality of the turntable can be judged by two specifications, wow & flutter and rumble (sometimes referred to as signal to noise). To judge the quality of a device you can compare these specs. The lower the number for wow and flutter the better. Entry level turntables would be at about 0.1% while very good ones get down to 0.025%. Rumble is a bit strange in that it is a negitive number. The more negative it is the better. So entry level is about -50 ~ -55 dB or so. Some of the best of the bread were able to make -75 ~ -80 dB or so.
The tonearm caries the cartridge across the record. There are very rarely any specs published on a tonearm and when there are it is rarely more then the effective mass. The use of that is match the tonearm to the cartridge to the tonearm to avoid resonance tracking issues. Minor issues caused by mismatch are common and usually take the form of the stylus skipping when you walk by the furniture holding the turntable. Major issues are the vibrations caused by the stylus tracking the groove of the record causes the skipping. I have only seen that once, and I've been part of this hobby since 1968.
The signal of the cartridge is very weak and needs two things to be useful, equalization and amplification. This is done by an RIAA preamp. This can be a stand alone device or can be part of either an audio preamp or integrated amp or receiver or an all in one as you have. The RIAA preamp takes the cartridge signal and boosts it to the level of another so called high level device such as a tuner of CD player.
Out of the RiAA preamp (or phono preamp if you will) the signal goes to the line level or control preamp. This is where your volume, balance, tone controls and input selector switching live. There is more gain in this stage but it's primary job is control of the input, volume and other audible effects.
From the control preamp the signal goes to the basic or power amp. The sole job of this section is to increase the strength of the signal and power to levels that can drive the speakers.
For a starter system, you would want to combine the RIAA preamp, control preamp and power amp in one component, either an integrated amp or a receiver which is a device that also incorporates a radio tuner.
The last piece of the chain is of course the speakers.
With your all in one box, your output that you tried to hook you speakers to is like the output of an RIAA preamp, it needs the control preamp and power amp to drive the speakers.
I know that is overload on one post for someone new to this and without knowing more about what you can afford and what your objectives are it is really hard to help you further.
Shelly_D