Yeah why would you use 40 watts or less? Surely using speakers that the impediance aren't less than 8 ohms you will be alright.
Speakers are usually rated on "acceptable amplifier range". So you'll see a speaker that is rated thusly.
25-100 watts recommended 200 watts peak.
This just means the manufacturer of the speakers suggests that you use their speaker with an amplifier that is between 25-100 watts continuous power. A peak power figure tells gives you a theoretical amount of power the speaker can handle in short bursts (not continuously).
As others have said, you should probably look for speakers that fall into that suitable power range. I'd probably go no less than 87dB 1w/1m for efficiency if you want to reach reasonable output levels. If you're looking to get crazy loud you'll need to push for something 93dB 1w/1m or better to achieve high output with only 40 watts to work with.
I will say this. First you had a Leak amplifier, now you have a Rotel integrated amplifier. It seems curious to me that someone that doesn't know much about home audio equipment keeps happening across decent midfi equipment but for whatever reason cannot find decent speakers.
Do you mind if I ask where your general location is? Where did you find this Rotel amplifier and how much was it?