What do you mean the old speakers no longer work? If it is the surround of the woofer, we replace those. If it is a tweeter, maybe there is a fuse or a replacement available on the bay. Otherwise just about any speaker will work and many look to the used market knowing they might have to install new surrounds in a nice 1x1x2-foot speaker like Advent, AR, ADS, or whatever. These are everywhere and ADS have rubber surrounds on most of their line that don't need replacing. Some like speakers that get loud with little power and these Cerwin Vega or Klipsch among others will also work and play a lot louder with the 30 watts per channel the 1060 will deliver. Of course, 30 watts is plenty for almost all listening in regular rooms except drunken, college party volumes.
So what speakers are broken and how broken, fixing can be the cheapest or you could find some nice bookshelf speakers (that 1x1x2 size and smaller) for cheap. If you don't need loud party speakers some of the small speakers out there would work fine for those college years, Polk, Infinity, Paradigm, NHT, half or less the size of the others mentioned and well those companies have smaller speakers, too, but as size goes down, bass response drops...so we add a sub.
Tell us what you have, where you want to go and where you are.