Good morning, and sorry for the late response.
That Polk has gotten a lot of good reviews on Amazon. That always inspires confidence in me. Some people really like Polk subs, some people don't. My friend got a smaller one than what you're looking at for about $100 years ago, and he's really happy with it. It sounded surprisingly good to me when I heard it. Quite nice for $100.
One thing to notice is that the -3dB point is listed as 40 Hz. The output of subs will drop off as the sound goes either higher or lower in frequency (I put a graph below from a completely different sub just as an example, but the numbers are pretty hard to read), and the point at which it is 3 dB lower than the average output is a typical value to put in a spec. You mentioned that you want "deep bass." For us to help you better, think about and let us know what you mean by that. If you want that punch or kick that bass can give, my recollection is that is from frequencies around 50-60 Hz (I forget exactly). If you truly want to go low in frequency, that Polk might not be the answer. The BIC that I provided a link for is rated down to 25 Hz, but it doesn't give the +/- dB rating, so it's tough to say (but based on one of the reviews, I have the impression that it does go lower than that Polk).
To get into the 20 Hz and below range in a commercial sub is going to cost more. I don't know the least expensive one that will do it, but someone here might. I'm a fan of a company called
SVS. I bought one of their subs back in 2007, and the customer service was outstanding - and so is the sub. They are an internet-direct company. They were recently purchased by another company, but people here still seem happy with them. Their least expensive offerings that go sub-20Hz are in the $750 range.
There are a number of threads on here related to the best sub for $X. I encourage you to peruse in the subwoofer forum here, or even post your own thread once you settle on a budget. I don't have much experience with subs out there these days, but people around here do.
Just let us know what else we can help with, and enjoy your shopping! It's always fun to get new gear.