Much depends upon how loud you want to be able to listen, at what distance.
Speaker sensitivity will be an important variable with a relatively low-powered amp such as the 2226. The greater the speaker's sensitivity (rated in dB), the less power you need to achieve a given loudness level.
For example, a 92dB-rated speaker will need only half the power of an 89dB-rated speaker to achieve the same volume. And only one quarter vs a speaker rated at 86dB.
Its sensitivity rating tells you how loud a particular speaker will get, in decibels, with one watt of input, at 1 meter. Note that while, for example, 86dB is quite loud, and may well meet or even exceed your needs as regards volume, you also need 8-16 times that amount - or more to keep clipping distortion from becoming a problem. An amp clips the signal (aka goes into clipping) when it can't deliver enough power to fully reproduce the signal.
Note also that loudness drops off fairly quickly with distance...about 4dB for each doubling of distance in a typical home setting. So if a speaker can produce 86dB with one watt at 1 meter, it will produce around 82dB at 2 meters and 78dB at 4 meters. To get back to 86dB at 12 meters, that speaker would need 8 watts of input (plus the availability of at least 8-16 times that for peaks). The exponential relationship between loudness and power requirement is important to appreciate.
In addition to assuring that your amp can produce enough power to achieve the volume (loudness) you want, with minimal clipping, you want to be sure that your amp can handle the impedance of your speakers. Just avoid speakers with a reputation for running below 4 ohms. Most speakers are rated at 8 or 6 or 4 ohms; this is a "nominal" rating. Actual impedance can vary quite widely with frequency of the signal. If you go with 4 ohm speakers, try to look up their impedance curve to see if it drops much below that; if it does, no go. BTW, many modern speakers, especially of the "bookshelf" or stand-mount variety have relatively low sensitivities and are rated as 4 ohm loads.
Once you've address the technical issues described above, speaker choice is just about entirely a matter of personal preference (and budget). Your budget of $2K is more than adequate to get a really good pair of speakers.
Cutting to the chase, I would suggest that speakers with a sensitivity of 90-92dB or higher are likely to meet your needs, unless you want to be able to listen at near-concert levels. I would also say that if you will only listen at moderate or lower levels, or near-field (close to the speakers), you can go even lower.
