I'm gonna hit you with three sections here, so please forgive my lengthy answer:
All of these numbers are sort of approximations and simplifications. That's because audio equipment, like guitar amps, operates across a range of frequencies, and all electrical and electronic components (to a greater or lesser extent) respond differently a different frequencies. So we're going to proceed with an understanding that a "1 Watt amp" has a rated output of 1 Watts into some nominal load impedance.
We say "nominal impedance" because the impedance of a speaker is different at different frequencies, so first we pick an appropriate frequency at which to measure the impedance, and then we round to a reasonable power of two (4, 8, or 16 ohms). It's more like different speakers are in different impedance "classes" or categories.
Now that we have a nominal load, we can connect the amp to that load, and measure the power that the amp can drive into that load at a certain frequency. That's the rated power output. It's a rating of the approximate power in a specific situation. Assuming all your ratings are calculated in a similar way, you can compare different power ratings to get a sense of the power of different amps, but don't spend too much time trying to perform exact calculations based on rated power output or nominal impedances.
Now that we agree that we are talking about simplifications and approximations, I can proceed without feeling like I'm being deceptive or imprecise.
When you double the load, you halve the power dissipation. If you know the impedance at which the power output was rated, then you can calculate the (approximate) output power at a different load. If we assume that the "1 Watt" amp was rated into a 4 Ohm load, then it will put out approximately 1/2 Watts into an 8 Ohm load and approximately 1/4 Watts into a 16 Ohm load.
Ok, good, so then the 16 Ohm load will be 1/4 as loud, right? No, not even close. First, dividing the power output by 4 is a drop of about 6 dB in power, which translates (except see the next paragraph) into about a 6 dB drop in acoustic intensity, but you need to drop by 10 dB to be half as loud.
But that's assuming that the different loads have the same efficiency, which is the measurement of how electrical power is turned into acoustic power. So it might be that the 16 Ohm speaker is so much more efficient than the 4 Ohm speaker that it's actually louder! But that's unlikely. Still, it might not be 6 dB quieter, or it could be more than 6 dB quieter.
TL;DR (too late!): The 16 Ohm speaker is generally your "quietest" option, but it might not be that much quieter when all is said and done. Better to choose the speaker that sounds best.
Some points to ponder:
- Classic rock "distortion" is usually a lot less gain than most people think it is. AC/DC sounds pretty gainy, but it's really not.
- Many classic rock distortion sounds are more about pedals than amps (Jimi Hendrix, Jimmy Page, Stevie Ray Vaughan), although some sounds are pretty much all amp (AC/DC being probably the best example).
- Tone chasing will drive you insane, because even with identical gear you'll never sound the same as another guitarist. Using famous tones as guideposts on your way to finding your own tone is a good strategy though. Just don't get too hung up on re-creating something you've heard.
- Opinion warning: That 1 Watt amp you linked to seems like more of a gimmick than a low-wattage, high quality tube amp design to me. It looks like the higher end manufacturers are creating all-tube low Watt designs using real power tubes (EL-84, 6V6, etc.) and coming in between 5 and 20 Watts, usually 12 or 15. On the more affordable end of this concept is the Ibanez TSA15H, which also has a Tube Screamer circuit built in (a gimmick but not a terrible one). Fender, Orange, and Engnater also have accessibly priced amps in this category.
- If you don't already have woodworking skills and/or speaker cabinet building experience, you might find making a 1x12" cab is a lot more involved than it seems.