In my opinion, "overdrive" is a bit of a lie. Whether it's a boost pedal, a fuzz box, an "overdrive" pedal, or a distortion box, these are all essentially gain stages that go in front of your amp. All of them shape the sound in several ways-- increase the amplitude of the signal ("gain" or volume"), alter the EQ, and add clipping (harmonic distortion). [Except clean boosts don't add any audible clipping.] Because of this, all of them have the potential to change the sound coming out of your amp in multiple ways-- because of how they are directly changing the signal coming from your guitar to the amp, and then how that altered signal is interacting with the first gain stage in your amp...and then how that further altered signal goes downstream and alters the behavior of the other gain stages in your amp, such as the power tube stage. The strength and clipping behavior of the signal that hits the speakers also changes the response of the speakers.
Hence depending on your particular guitar, how hot its pickups are, and your particular amp/speakers, and how loud you like to turn things up, it is extremely hard to figure out what pedal interacting with your turned-down amp will simulate, at a lower effective volume, the sound you previously attained at a higher volume plugged straight in to that same amp. And that is before factoring in how the human ear hears things differently at different volumes. (Hence the loudness button on stereos).
So what happens is you typically get some suggestions from people who have had good luck with a particular amp with a particular guitar. But maybe they are seeking a different tone, or play at a different volume level, or use a different guitar/different pickups. So you have to start somewhere but this is why so many of us end up with a dozen or more dirt boxes. It is very hard to get there, especially if you are picky. Going with an "overdrive" is probably a good place to start, but good luck, young Padawan, and may the Force be with you.
One reason why so many people say RAT on this blog site is that it has a wide range of adjustments, with other fixed parameters being serendipitously pretty good for a wide range of applications, and so you have a better chance of dialing in the tone you seek. There are other pedals out there that seem to have a high degree of versatility, so that might be a way to increase the odds. Another clue I might offer is that at bedroom volumes you are likely getting all of the clipping from the pedal, not your amp. At that point the right "distortion" pedal has just as much chance of getting you what you want as the right "overdrive" pedal, and a "clean boost" pedal is likely to fail. A pedal like a RAT ranges from slightly dirty boost to overdrive to distortion to quasi-fuzz, and hence its potential to deliver the goods at a wide range of volumes-- it can goose the amp to get it to clip more, or it can do all the clipping itself.