What multimeter / functions to look for...

I would go for the best Fluke in your budget. I use them at work ( ind. electrician ). I also have an analog Simpson if the need be. Flukes are built tough and are rated for higher voltages.

$20-30 for an analogue multi meter. The needle on an analogue meter can tell you more than a digital one. They are cheaper too. I have had good luck with the ones from Lowes (don't recall brand at the moment). If you have an electrical supply warehouse in your area you can get the uber fancy ones that tell you things like distance to line breaks and the like. For a hobbyist the $20-30 one from Lowes should do.

Good luck!