How to select a subwoofer

My current system is shaping up nicely. My next step is to decide on a sub to obtain deeper and tighter bass. My speakers go to 25hz and my room is 14wx22lx9high. I enjoy classical with other genre. The issue of budget is always a question and it should be below 3,0000. Different companies have various setups so I would like suggestions that you enjoy. Thanks, Steve
I have the Tyler Acoustics Linbrooks Signature Towers. The bass is nice yet very low bass could be improved. The bottom end is reported as 25hz. Thanks, Steve

Is that bottom end being reported as 25hz according to the manufacturer's specs or some measurements that were published in a magazine?

I'm asking because manufacturer's specs are usually on the optimistic side and magazine specs show what they got under their test conditions, which are not likely to be the same as your conditions.

In any event, a sub will likely help you to gain what you seek. The most important part of getting a sub is finding one that will blend with your speakers.

If music is your greatest concern, I'd suggest that you get a sealed sub. Sealed subs typically don't go quite as low as a ported sub, but the bass will be better defined and faster, all other things being equal.

Although my only long term, in home experience with a REL sub has been my little T3, I do have to say that REL's use of the Nutrik connector to connect directly to the amp's speaker terminals made the sub easy to integrate into my system. REL's explanation of the use of the high level input is that this allows the sub to represent the bass in the same character as that which the mains are receiving. All I can say is that in my modest system, the integration is seamless.

I'd also check out the SVS subs. I've never owned one, but they are on my short list of equipment to check out. With your stated budget, you may be able to get into a pair of them.