Your Honda has solid lifters that probably need adjusting. It's not too difficult to do yourself (buy a book), and it's not extremely expensive to have a dealer/Honda mechanic do either, I'd guess around $100. That
should quiet down the idle. Your cranking problem might be caused by a failing igniter, which is basically the internal electronic sensor in the distributor that tells it when to fire. Does it ever fail to start when the engine is hot? It's a very common failure on this engine. That part is also about $100 at the dealer. Because it's such a common failure, I wouldn't recommend trying to find a used part.
Good luck with the CRX.
P.S. From your description of the noise, maybe you should have the oil pressure tested also, just to be sure.