Generally you must not charge with over 4.7V, do not charge past 4.2V on the battery, do not discharge past 20% capacity, and you must watch for overcurrent, undercurrent. These things can all be done with passives, but the amount of component and space for keepout space of each one can get quite large compared with IC battery chargers. Look up PMICs on a part suppliers website and you will get loaded with plenty of LiPo chargers. They can range from under a dollar for a TI part, to over five for an LTC piece. You just have to choose them according to your charging specs and choose their passives according to the charge current you want.
Look into the LTC4053. Very simple and you change the passives from PROG to change the charge current. It also utilizes trickle charging once your phone is full.
As for getting the required voltage out of your battery, you could certainly use a buck convertor. I would just recommend getting a higher voltage battery myself.