18650 or 2X 123 fit perfect in a plastic dime holder. From ebay. $.69
http://shop.hobbiesdepot.com/One-New-Coin-Safe-Square-Coin-Tube-Dime-Size-1-UNIT-CH-T-DIM-SQ.htm
Run caps are designed to stay in the system, they dissipate the heat.( Usually metal can). More microfarads means start faster, more inrush current. Different voltages for different supply voltages ( help keep cost and size down when not needed). On 120vac peak is 169v.
If you are blowing caps...
See if you can find a run cap. ( metal can). Caps only last so many starts. But if they have a big load when starting they burn faster. I maintain 100 small motors at work.