Integrated tube amp under $1000 / $2000

 I am very happy with a 1965 Sansui 1000A Receiver/Integrated amp at 40wpc RMS. Completely restored by Decibel Audio of Chicago. Sounds amazing with my Sansui SP-2000 speakers. Has 21 tubes in total with 2 very heavy Hashimoto transformers contributing to its weight. They do appear now and then on eBay. Need complete recapping. Early 60s were the peak time of tube technology after which transistors took over. I am sure Klipsch can be driven by them, unless they require amps above 200w. Also worth looking for Sansui AU-111 which is an integrated amp from the same era, though it probably will be more than 2k. 

I like Primaluna because I have had good luck with mine. Easy on tubes. NO biasing. Quiet and as black as about anything I have heard for way more money. Good power for the rating. They hold value very well so if you want to move up in power - (why?) - it is a lot cheaper to do.

+4 for the Quicksilver. Quality, sound, value and a great match for the Klipsch. 

try a second hand DK unit

$1000-$2000 is a good budget for exploring tube amplifiers.   Cayin, Rogue, Prima Luna all get rave reviews and are readily available both new and used.   I would also suggest Icon Audio.  This company is not well known in the US, but very well known and very well regarded in the UK and EU.

If you are patient and lucky, you may find a Line Magnetic integrated amp within your budget.

The used market provides a lot of options.  Several Audio Research and Conrad Johnson models should be easy to find.

Personally, I would look for a vintage tube amp.  Such and amp would be a GREAT match for Klipsch speakers, and unlike just about all of the above, a used but restored vintage amplifier will retain value, and may appreciate.  This can be crucial consideration if you want to buy-try-sell-repeat several times before finding an amp to live with.

Caveat is to be sure to purchase a carefully restored amplifier- from a reputable seller, and preferably with a warranty.

Fisher X202, or X1000   Scott 272 are both well regarded integrated amplifiers.

Fisher 500c or 800c are universally regarded as 2 of the finest receivers of the golden era.