My BIL has this full house speaker system:
http://img.photobucket.com/albums/v318/annewaldron/45BF69B8-AE68-4D1D-B050-31BBE5D9275C_zpsjev8glzs.jpeg
He had a 100W receiver which I believe he ruined trying to power these speakers- not enough wattage?
I know zero about this type of stuff, but I’m hoping a smarter doper can help me understand what type of receiver is needed to power the above.
P.S. My image link formatting is for the birds, apologies!
An underpowered amp is more likely to damage speakers than to be damaged itself. When you connect a low-powered amp to inefficient speakers, the user will tend to turn the volume up high, which can lead to clipping. A clipped signal has a lot of high-frequency energy, which can burn out the tweeters.
This happened to a friend of mine years ago: he had a pair of AR-9 speakers, which are famously inefficient. When his high-powered amp went into the shop, they gave him a low-powered amp as a loaner. He ended up having to replace the tweeters in the AR-9s.
Looking at your picture, I believe the power rating on the box is for maximum power, not minimum. That is, these speakers are able to take 50 watts of continuous power, and 100 watts of peak power. A 100-watt-per-channel amp should be able to power these speakers with no problem.
Did your BIL by chance use several of these speakers and wire them in parallel? (He should know this, if you don’t.) If he did, then the problem is that the total impedance of the speakers is too low. Three 8-ohm speakers in parallel will present a load of about 2.7 ohms, which is very bad for most receivers. They are designed for 4 to 8 ohms (two speakers or a single speaker) on each channel. More than three speakers on a single channel is very, very bad.
There are ways around this, but I won’t go into details unless this is actually the cause of his problem.
More power won’t help if the impedance is too low. Some (but not many) power amplifiers are designed to handle low impedances, but receivers generally are not.
As to your original question, I tend to use Yamaha receivers, but there are several different series (casual use up to very good quality) and you have to select one carefully based on need. But a good quality Onkyo or other brand would work just fine as long as your BIL doesn’t wire too many speakers to the outputs.
[Moderating]
Requests for recommendations fit better into the IMHO forum than GQ. Moving.
A friend of mine had wired several speakers for some church program, and they were barely audible. I think there were four in parallel. Two in series connected to the other series pair in parallel got him back to four ohms.
This is to be expected. The problem with wiring two speakers in series (for 16 ohms effective) and then another pair in parallel is that you get a 50% voltage drop across each speaker. Voltage is basically equivalent to volume (not really, but the concept is easy to understand) and so you end up with each speaker producing much less sound. There really isn’t any such thing as a free lunch when it comes to sound systems.
If somebody really wants to distribute several speakers around a building or a house, get a paging amplifier with a 25 or 70.7 volt output. Use multi-tap speakers with transformers that convert the higher voltage to current (again…this is taking a complex subject and reducing it to a simple concept). This makes the total impedance much less of a factor.
I had about five minutes before the parishioners tore him apart. 
