Preamp/Subwoofer connection question....

You can try a digital crossover like the Behringer DCX2496 ($350) or the DBX Driverack ($499), which is what I have. You will be able to adjust both the high pass and low pass settings between your speakers and sub to get the best from both. You can bi-amp your speakers with another amp, if you want. Also, there is a seperate microphone available that you can use to EQ your room.
One of the problems in using just a pre with multiple outputs is that there is no crossover to stop the speakers from trying to play the lower frequencies although usually the sub has one so it will not play high freq. I learned this the hard way, I blew out a driver while playing a movie with some really loud low freq. sounds.
These digital crossovers are balanced which makes them ideal for fully balanced systems. But they can be used single ended if you get XLR to RCA adapters.
Sonny

If it's good enough for you, the NAD c160 has two pre outs. I have it , and I like it. It can be had in your price range.

B&K PT-3 and above has a sub out and crossover.

Any main output from a preamp will work to the subwoofer line in (high level input). Many preamps have a pair, or more, of stereo main outs. This allows the preamp to drive up to three stereo amps in a bi or triamp mode or to drive an amplifier and a subwoofer.

Many subwoofers only have ONE RCA line level input; ie, no stereo inputs. In this case you just get a 2 into 1 RCA adapter and then run one RCA interconnect to the subwoofer. Monster Cable makes a decent quality adapter. In fact, I have several of them I no longer use and would sell for about ten bucks. The Radio Shack type things are real junk.

Most subwoofers also have speaker inputs. All you do is run an extra set of speaker wires from the amp speaker outputs to the subwoofer in addition to the speaker wires to your main speakers.

Many subwoofers will offer a line out or speaker out and these outputs are intended to allow you to simply put the sub between your amplifier and the main speakers and you route the high frequencies to the main speakers and only the low frequencies to the sub. Typically, this will allow small main speakers to play louder and with less distortion. That is the good news; the bad news is that most crossovers inside powered subwoofers are junk and not to be used as it adds another active stage to the signal that has already been amplified by your amplifier. Best method is to run the sub in parallel with the main speakers. Another method is to acquire a quality active crossover and not use the internal crossover of your sub. Of course, in order to do this effectively your sub would have to have a way to defeat/bypass the internal crossover.

Hope that makes sense.

Phasecorrect, some to many preamps these days have two sets of main outputs. I use the pre's XLR main outs to the amp. When I did own a subwoofer, I used the single-ended main outs for the sub.

As for the price range you mention, I can't help.

-IMO

Most subs will allow you to connect via speaker cables from your amp, and there are different ways this can work. Infinity's usually run speaker cables from the amp to the sub and then to the main speakers, and filter lows off from the main speakers (unswitchably.) REL gives you a proprietary cable with connector which runs from the same speaker binding posts that your main speakers' cables do. The RELs supplement the main speakers in this hookup method, without keeping the lows from reaching the main speakers. Vandersteen subs _only_ hookup via speaker binding posts, unlike the other two examples (as well as most subs) the Vandersteen models give no RCA/line level option. You could see the hookup box and filter theory notes at the Vandersteen web site; it's not like anything else.

Finding a decent ss pre in that price range is hard, period. I don't see why a pre can't be tube - the voltages are so low you avoid most of the drawbacks of tubes. For examply, if you can live with the service risk, norh makes a nice, cheap tube pre with pre outs. So does Antique Sound Labs. Of course, if you're asking for a preamp for use with a sub via RCA/line level out it's better if the preamp has two pairs of pre outs.

There are passive preamps which fill your requirements, and they might sound good. For example, redwineaudio.com.

IRD has a decent pre with sub jacks, but it's $150 or $200 more than your stated limit.

I'm sure there's no limit to suggestions, but this will get you started.