Aqua power is going to be the easiest to harness, especially with the (Personal opinion: Ridiculous) restriction of no mining.
Without any organized industry (Opinion the same as the above), you can't make anything remotely like a steam engine or internal combustion engine. They're just too complex and require tools and equipment that can only be had by industry.
I'm not sure you could get electric lighting without industry, as incandescent light bulbs require the filament to be in a vacuum - And without industry, a vacuum is hard to make. Not to mention, without industry you can't really have the glass for the bulbs either.
Tim B II has a good method for storing the energy, which can work for even non-electrical things - Smothing out the gearing of a water mill to provide constant power for things like looms or grain grinding. Lead-acid batteries, as mentioned by Thorne, are also fairly easy to make.
Thorne also mentions Radio. Basic radio is possible, but would require, again, some amount of industry.
I would recommend that you allow a small place to have some industry, some mining, etc. In one of your other questions, you mentioned a University as maintaining knowledge. They would also be the prime location for small amounts of industry - As they know how to make things, how to maintain them, and as you've mentioned they can and do trade out knowledge of things, they could also be the source of things like radios and electric lights.
Additionally, small industry of the sort you would need is fairly straightforward to accomplish, especially given your time frame. A University will have many, many experts on many things - And, more importantly, it'll have exactly what is needed to learn about other things. A bio-plague is also more gradual, so it could have started on the opposite side of the world. It wouldn't take much of a leap for someone at the University to think "Hey, we're going to need to hoard these tools" and "We're going to need to make X, Y, and Z." There's also the fact that, at 60 years post-apocalypse, you can even have some people still around that were young (20-30s) when the apocalypse happened. Old Greg might be 80, but he's the one that set up the light bulb factory and still makes the best ones.
Also, to address whether things can be found and be functional after 60 years: This is all based on my expectations and basic knowledge, and not on any research, but the primary killer of incandescent light bulbs, and a lot of other technology, is vibration. The lights in the ovens at work are constantly dieing because they're right inside the door, on the latch side. A different store has ovens largely identical, except the lights are on the hinge side. Those lights last significantly longer than ours. How is this relevant? Well, it goes back to how your apocalypse happened. Meteor impact? Lots of vibration. Tsunami? Vibration. And water. Bad for tech. Nukes? Vibration and radiation, both bad for tech. And that's not even counting the EMP. Yours? Well, it's a bio-plague. Significantly less vibration caused in specific areas means things are more recoverable.