Peak charging is something NiMh, NiCd does, lipo uses a charge protocol called C/CV and yes, charger using lipo mode will automatically shut down when the CV phase of the charge is finished. Would advise reading about lipo so you can handle them knowledgeably and stay safe with them -


http://www.rchelicopterfun.com/rc-lipo-batteries.html


For a charger, consider the Thunder AC-6 sold by Hobbypartz. Its a good charger, plenty in use here, won't break the bank and has a good rep -

http://www.hobbypartz.com/thac6smbachw.html