Recommended Speaker for Triode Amp

I've been living with inefficient Thiel 3.6 speakers for many years now, but now I'm getting a new integrated Triode amplifier rated at 20 watts per channel. I'm not familiar with horn and open baffle speakers, or other inefficient designs and could use some help.

I listen mostly to jazz, female voice, acoustical types, and rock, as opposed to Big Band and orchestral music. I have a fairly small listening room. I do like my bass, so if it's there I want to produce it well.

I've seen some speaker kits and I am handy but don't have a lot of woodworking tools. For example, I would not want to cut those large round speaker holes.

I also don't understand how to match a speakers efficiency to the power output of an amp, or maybe that doesn't matter as long as you can drive the speakers to loud levels.

I do have two goals. The first is to spend between $3K to $6K tops, and the second is to smoke my Theil 3.6 speakers.

Help and recommendations are appreciated.