Phono grounding when using integrated w/ floating ground?

I use my integrated's phono stage. The amplifier is a floating ground design (no ground prong). My turntable has a 3 pronged plug. The outlet everything is plugged into is grounded. My question is thus:

Should I use the grounded power cable for my turntable, or buy a 2-prong power cable? I wonder if issues could arise if I ground the TT to earth *and* to my integrated? Conversely, I could ground the TT to earth and forgo the ground wire to my integrated.

What is considered best practice here, or should I just experiment? Thanks!
Power in a 110V circuit is one hot and one neutral. Neutral is also ground. The only difference is the path it takes to ground. But its ground. Which you can see if you look at the wires behind the panel. So your integrated is grounded, only just once not redundantly like it would be with the 3rd ground wire connected. That third ground is a rod into actual ground. 

A lot of homes were built and are to this day still wired with only the two wires, hot and neutral. Yes you should use your grounded power cord with the turntable. Always use the best power cord you can, grounded or otherwise. My Herron phono stage uses a grounded power cord, even though you can see inside the ground isn't connected to anything. The cartridge is still grounded to the Herron even though the Herron isn't grounded to anything. (Not even neutral. Long story.) 

So anyway, perfectly safe either way. Hum however will probably be lower grounded to the integrated. That way all paths to ground- cart and RCAs- are the same. Multiple paths to ground are an invitation to hum. Doesn't always happen but its a risk.
@ lostark

You don’t need the AC mains safety equipment ground.

The ground for the TT arm is the circuit ground of integrated amp.
Just connect the ground wire from the arm to the ground lug on the amp.

So your integrated is grounded,
Not necessarily. If there is no chassis ground, and the live and neutral are isolated by the power transformer in the amp, then there is no safety ground or direct path to true ground. The manufacturer has ensured the amp is double insulated and does not require a safety ground.
In your set up, the amp would be grounded through the turntable ground wire only; thereby ensuring no ground loop.
Look Mom, no power cord!

Grounding Myths

From Henry W. Ott’s  "Electromagnetic Compatibility Engineering"

3.1.7 Grounding Myths

More myths exist relating to the field of grounding than any other area of electrical engineering. The more common of these are as follows:

1. The earth is a low-impedance path for ground current. False, the impedance of the earth is orders of magnitude greater than the impedance of a copper conductor.

2. The earth is an equipotential. False, this is clearly not true by the result of (1 above).

3. The impedance of a conductor is determined by its resistance. False, what happened to the concept of inductive reactance?

4. To operate with low noise, a circuit or system must be connected to an earth ground. False, because airplanes, satellites, cars and battery powered laptop computers all operate fine without a ground connection. As a mater of fact, an earth ground is more likely to be the cause of noise problem. More electronic system noise problems are resolved by removing (or isolating) a circuit from earth ground than by connecting it to earth ground.

5. To reduce noise, an electronic system should be connected to a separate “quiet ground” by using a separate, isolated ground rod. False, in addition to being untrue, this approach is dangerous and violates the requirements of the NEC (electrical code/rules).

6. An earth ground is unidirectional, with current only flowing into the ground. False, because current must flow in loops, any current that flows into the ground must also flow out of the ground somewhere else.

7. An isolated AC power receptacle is not grounded. False, the term “isolated” refers only to the method by which a receptacle is grounded, not if it is grounded.

8. A system designer can name ground conductors by the type of the current that they should carry (i.e., signal, power, lightning, digital, analog, quiet, noisy, etc.), and the electrons will comply and only flow in the appropriately designated conductors. Obviously false."

Henry W. Ott