Carpet padding is entirely inconsequential for subwoofers. Do whatever you like with the carpet padding. To affect bass from a subwoofer, you need bass traps that MUST be 5 to 8 feet long in at least 1 direction, The wavelength of 30 Hz, for example is 10.3 feet, so a bass trap capable of controlling 30 Hz has to have one dimension that is at least 5.15 feet long.
You will literally drive yourself insane trying to setup a subwoofer without having an SPL Meter. You really MUST have one. Be sure you get one capable of accurately measuring 16 Hz--or one that is provided with a correction table that might look something like this:
30 Hz +2 dB, 25 Hz +4 dB, 20 Hz +6 dB, 18 Hz +5 dB, 16 Hz +8 dB. What that table means is if you measure 20 Hz at 70 dB on the meter, you hav to add 6 dB to that measurement to get the accurate measurement of 20 Hz. So your 70 dB measurement is REALLY 76 dB.
The next thing you use the sound pressure level (SPL) meter for is to find the ideal spot to PLACE the subwoofer. The main problem with that is that you would probably be tempted to put the microphone where you sit, and move the subwoofer to different locations followed by recording a series of measurements from 16 Hz to 100 Hz or whatever your top frequency for the subwoofer is. Your best position will have the fewest and smallest variations in your measurements for each frequency. This is brutally annoying to do in a room with "stuff" in it. I will suggest a radical solution that will speed the process dramatically... place the subwoofer where you will sit... right on the sofa or chair--just don't block any radiating surfaces of the subwoofer--and don't block any ports on the subwoofer either. Run a set of measurements where you would LIKE to place the subwoofer. If there are big differences at different frequencies, move to a different convenient location -- if the response is still lumpy, try moving the SPL meter to a different location. The height of the meter for the measurements should be about equal to HALF the height of the subwoofer. So if the subwoofer is 18 inches tall and the radiating woofer is in the middle of the cabinet, you'd want the SPL meter 9 inches from the floor and aimed vertically at the ceiling. If the subwoofer is 18 inches tall, but the woofer is closer to the top of the subwoofer than to the bottom, you might need to put the SPL meter at 10 or 11 inches off the floor. OK, if none of the "easy" locations produce a reasonably non-lumpy response (all readings within a 10 dB window is pretty **** good for a subwoofer).
There is a room dimension interaction with every subwoofer... in fact, there are 3 room dimension interactions with every subwoofer. The height, width, and depth of the room can interact with the sound produced by the subwoofer causing a cancellation that can make it look like some spots in the room have NO BASS at that frequency. This is called a room cancellation. If your height dimension, width dimension, and depth dimension are all the same, you have a TERRIBLE room for bass response. So a room 15 feet x 15 feet with a 15 foot ceiling... terrible room for bass. Even having 2 room dimensions the same can be problematic. The best scenario is if each room dimension is different. It is better yet if each room dimension is not divisible by the same number... so a room that's 12 x 14 x 16 may seem good, the fact that you can divide each dimension by 2 is a bad omen for getting good bass. 9 x 18 x 27 would also be a "bad" room because each dimension is evrnly divisible by 9 or 3. If you have a CHOICE about the room dimensions, having them prime numbers is a good way to go... 11 x 17 x 23 for example. When a room dimension interacts with some frequency, you can end up with a cancellation effect that is profound. You might be measuring 70 to 80 dB everywhere except 1 frequency you measure might appear to have no sound at all because the cancellation effect is so profound. It's just a room dimension causing that problem, so move the subwoofer a bit. I suggest moving the subwoofer 6 to 12 inches... not less than 6 inches while looking for a good subwoofer location. This whole process is so much easier if your test tones can be controlled with a remote control or tablet/phone/laptop. You want to avoid placing the subwoofer anywhere that there is a strong cancellation. There is NO FIX for room cancellations except for moving the subwoofer away from that spot.
The beauty of moving the SPL meter is that you can place it in locations that may have other objects without having to rearrange the room for each measurement. When you eventually find a spot where the SPL meter produces reasonable measurements, put the subwoofer there, and move the SPL meter to your main seat then repeat the measurements just to confirm that you found a good spot at last.
Picking a subwoofer is entirely dependent on the speakers you will use... specifically, the SMALLEST speakers you will use. If you choose speakers that are "done" producing sound at 120 Hz or so, your subwoofer MUST have a driver with low-enough mass to be able to reproduce low distortion sound at 180 Hz... because you don't want the subwoofer to give up at 120 Hz if the speakers also give up at 120 Hz. You have to have at least 1/2 of an octave of frequencies overlap between the subwoofer and other speakers. If you use small speakers that run out of gas at 120 Hz, you will set the crossover at 150 Hz from the subwoofer to the other speakers. An octave is ANY doubling of frequency... 33 Hz to 66 Hz is an octave. 100 Hz to 200 Hz is an octave. 6000 Hz to 12,000 Hz is an octave, 444 Hz to 888 Hz is an octave. The crossover slope for the subwoofer will probably be 12 dB or 18 dB per octave. So if the subwoofer crossover is set to 100 Hz, at 200 Hz, the subwoofer would be "down" in response by 12 dB or 18 dB but it would still be making sound if the SPL level was 80 dB average. BIGGER speakers can use a lower crossover point. If your speakers are -3 dB at 70 Hz, you can set the subwoofer crossover to 100 Hz to get the overlap you need.
There is 1 RADICAL shortcut to subwoofer placement that works 100% of the time and is AUTOMATICALLY the best place in the room to place the subwoofer. Put the subwoofer directly behind your main seat, almost touching the seat... get it as close as possible to your main seat. This means your direct sound from the subwoofer will overwhelm any room effects and you will hear the most linear bass you can POSSIBLY achieve in any room. This works best with subwoofer crossovers of 100 Hz or lower. So using speakers that are -3 dB at 70 Hz or lower is ideal for the near-field placement of the subwoofer. You will always hear the direct sound from the subwoofer before it has an opportunity to interact with the room. Obviously, you have to be CAREFUL setting the level of the subwoofer when it is that close so it doesn't become overpowering. That's another place the SPL meter helps you. You can measure, say 300 Hz, and 50 Hz and adjust the subwoofer level so 300 Hz and 50 Hz have the same reading on the SPL meter. A lot of people reject this location for the subwoofer without even taking a shot at using it because they think it MUST be WRONG. But they are all incorrect. If you can manage nearfield subwoofer placement, you will automatically get the best bass you can get in your room because you are so close to the subwoofer, the room is kind of removed from the equation.
Small speakers require a sub on the small side... 10-inch driver or 2 8 inch drivers would be the best choice. You also have to decide whether you want a sealed-box subwoofer or a ported subwoofer. Sealed-box subwoofers sound best with music, but it is **** difficult to find any sealed-box subwoofer that can produce bass much below 22 Hz... and it will begin rolling-off bass response at 30 Hz. Even if the sealed box is kind of large, it might still only reach 20 Hz at 5 or 6 dB below 30 Hz dB level. I solved this by getting a subwoofer with 2 ports and 2 plugs for those ports. I remove 1 plug for movies and TV shows, and I put that plug back in for music. 2 plugged ports turns the subwoofer into a sealed box subwoofer. If your budget-limited for the subwoofer, I heartily recommend Hsu Research VTF-3 in whatever the current configuration is. Mine has a 15-inch driver in a larger than average cabinet... and it is FLAT in my room from 10 Hz to 110 Hz. You cannot hear 10 Hz at all, but when I play a 10 Hz test tone, it feels like somebody turned-on a large fan and the SPL meter still response to the 10 Hz wind as though it is an audible frequency. Needless to say, 16 Hz is reproduced at the same level as 80 Hz (1 port plugged, 1 port open)... it is an astonishing accomplishment to get that kind of bass response from a sub-$1000 subwoofer. You only need 1 subwoofer if your subwoofer is THAT good. The only reason you'd ever need 2 subwoofers is to cancel a room mode (bass suckout at some specific frequency) you cannot avoid for some reason. One Hsu Research subwoofer has been plenty for the last 3 rooms I've had (19.5 x 23.5 x 10.5 and 20x24x 8.5 and 13 x 28 x 8.5 all in feet). It will play louder than I need and I found a great location in each of those rooms where there has been little or no bass suckout problems.
To experience 10 Hz bass in your theater room... in the movie called Edge of Tomorrow (Tom Cruise, Emily Blunt), at the beginning of the movie while the opening credits are still running... when the Village Roadshow (one of the backers of the movie) appears, a bass frequency sweep begins at about 40 Hz. That frequency sweep goes lower and lower and lower until it finally ends at 10 Hz. If you feel wind in your room at the end of that sweep, you'll know your subwoofer is reproducing 10 Hz.