The display profile (the p3 profiles) and the document profile are two different things, serving different purposes. Do not use the display profile as document profile. That defeats the whole purpose of color management.
The purpose of the display profile is to be an accurate description of the display's actual and current behavior. So you use whatever system display profile is the closest to how your display actually represents the numbers. Having one made with a calibrator, based on actual measurement, would be much better.
The document profile needs to be a standard color space, traditionally, sRGB, Adobe RGB or ProPhoto. However, it has become increasingly common in the Mac community to use Display P3 everywhere - not really what P3 was intended for, but given that this is becoming common practice, Display P3 should be included in the list of standard profiles.
Next, to get a preview of what the file will print like, you proof to the print profile. The printer will need to tell you what their print profile is. It sounds like this is going to be printed on an inkjet printer, not offset, which is why they're asking for RGB and not CMYK.
The purpose of proofing is to show you on screen what colors in the file are out of the printer's gamut. It restricts the on-screen representation to the gamut of the print profile. Ultimately, the printed result is limited by the physical properties of the specific inks on the specific paper, which is reflected in the profile. If it's a high-end inkjet printer, you may not see a very dramatic difference. If it's offset, expect a severe dulling down of many strong colors.
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That was the color management part. There's a second part, which is display calibration - white point color and luminance, and black point. Monitor white should be a visual match to paper white, and monitor black should match max ink. This is a purely visual match - if it looks right, it is right. Most displays out of the box are way too bright and with much too high contrast (too deep blacks).
Since you don't have a calibrator, numbers won't tell you anything. Just adjust brightness until it looks right. If you get it right, what you see on screen will match the printed result.
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