The batteries on those little Shox speakers seem to last for ages before having to recharge. I find tho if you run an Ipod as your player with them the sound is too soft (I love it loud).
As for speakers, the cheap ASC speakers are best. I had them in the open and could hose them down. As for radios, the boss head hidden away with an external remote.
I'm with you on this. I got a DIY amp kit from Electronics 123. Solder a 3,5mm stereo jack onto the L&R inputs, seal the whole thing up in a small housing (also available from them) just be sure to cut out the back of the housing and mount the heat sink so that the fins are outside and able to cool the ICs. Then get some waterproof speakers. If you are not competent with a soldering iron, take it to an electronics repair place and ask them to build the amp for you.