'Optimum' is a moving target that's dependent on the needs of the app, but from a technical POV, a max flat impedance is the optimum, so Fs/Qts will define its Fp. From this we see that to get down to 25 Hz with authority will require a <25 Hz Fs driver with a Qts up to ~1.0 and preferably around 0.7 or a bit less depending on the driver's Fs and any room loading effect. Also, with larger pipes the driver's Vas needs to be enough to fill it up, a real problem with many drivers today that are designed to work in teeny-tiny cabs.
I already built TL sub back in 2006 with not so good driver for TL, but the result is affordable good for my ear.
Now, I have time to replace it , but this time I want better result by carefully choosing a driver that is fit with TL design.
So for my need, the driver should be:
1. Fs<25Hz , is it correct, lower is better?
2. Qts<1 , preferable 0.7 , what if lower than 0.7?
is there any other T/S parameter to be considered?
Right, you ideally want Fs to be at least as low as the lowest you want it to go and if it has enough power handling, then a little lower.
Just like with a typical vented alignment, the lower Qts is, the higher its F3 will be if not EQ'd.
As I noted, low tuned TLs with any decent output are large, so the driver's Vas needs to be high enough to 'fill up' the TL. If it won't, then a hybrid is required, i.e. place the driver in a box and add large/long vent. Another way is to use a reverse tapered TL (TQWT).
For instance, the Exodus Audio Shiva X2 has a ~21.3 Hz Fs, but only a 97.12 L Vas, so tuned to 21.3 Hz the TL's area isn't large enough to mount the driver and with a ~0.39 Qts, yields a ~26 Hz F3 in half space, though of course it will be considerably higher if stuffed.
A large enough TQWT to fit the driver comfortably in will be ~20% larger though.
Unfortunately, you have to design it first to find out what each driver 'wants' in the way of acoustic impedance loading. Now that MJK has developed a relatively simple 'classic' TL designer complete with driver offset suggestions that another DIYer turned into an Excel SS to make it even quicker/easier, it doesn't take long to find out if the driver will comfortably fit (typically 3-4x Sd) and software to fine tune it if need be using an old MathCad demo available from his site: Quarter Wavelength Loudspeaker Design
WRT driving position, for a (sub) woofer that's limited to ~ two octaves, i.e. its HF limit is ~ 1WL away from Fp, then end loading is best since it yields the maximum gain; otherwise, offset is usually best overall since it trades max gain down low for a smoother response over a wider BW with less stuffing density.
For 25 Hz then, 25*2^2 = ~100 Hz upper usable limit for end loaded and by 'end loaded' I mean it can be mounted either on the top plate or end of a side plate.