Do I need a pre-amp?

From what I see you will need at least an external phono stage for this receiver, which you could run into one of the analog inputs. You cannot just run the turntable into the unit, it needs to have the RIAA equalization of a phono stage. No need to go overboard on your phono stage, there are a lot of inexpensive units out there that members can recommend (I got my son a Creek unit to use with his A/V receiver) that will do the job for you.

The Sonograph is an older table (in its day it was a good starter table) but I think, as long as it's in good working condition, it will work just fine for your purposes at this point.

Rcprince is correct. You need a phono preamp and your Marantz doesn't have one. Since you're new, I would just buy all 3 as a package from a dealer that's good with TT's.

Lion

Not mentioned is you need a preamp for a moving magnet cartridge, not moving coil (you will run into both when looking for phono preamps). If you buy the setup in your link.

Moving magnet cartridges (the device that plays the record, mounted in the end of the tonearm) generally put out higher voltages (nominally 3-5 milli-volts or .003-.005 volts at 1 KHz) and are therefore able to use phono preamps that are a bit cheaper.

Moving coil cartridges generally put out a lot lower voltage (a factor of 0.1 or 10% of the MM) and therefore need a much lower noise (ergo more expensive) phono preamp.

Some phono preamps can handle both MM and MC cartridges.

Moving magnet cartridges are sensitive to cable capacitance so you should be aware of this when you buy a phono preamp, as its input capacitance adds to the cable capacitance (of the cables from the cartridge through the tonearm to the phono preamp) to "load" the cartridge. The cartridge manufacturer will specify the recommended load capacitance. If you are too far from recommended ranges, the sound may be affected.

Now, aren't you glad you are getting into vinyl?

I have owned a SG-3 since 1983. It was a great starter turntable then and if in good condition still today. As stated above, you will need a phonostage. I would stick to the moving magnet type cartridge as there are greater choices in carts and stages within your budget. Good luck in your search.

I think, you are looking in the right direction when you say that your analog set-up should not be weaker than your speakers. At least. Turntable isolation/resonance control is very important, even more so since you are using a subwoofer.
You might also consider older direct drive Technics with, say, Grado Gold cartridge. Just a thought. You can probably get for $100-$150 acceptable used phono pre-amplifier for Moving Magnet cartridge.
And you will want reasonably clean records and stylus, or all this will be for nothing.