Re: Replace 'BallCock' style with newer 'Flush Valve' style ?
If you toilet tank is typical of others, this should be pretty painless for you. If the supply for the tank is feed into the bottom of the tank, and then this goes into the "toliet fill valve" (the vertiacl tube) which has the ballcock arm. Then you will be able to replace the entire inside guts of your toilet tank with little problem and about $30.
Go to the hardware store and pick out the replacement toliet fill valce you want. Also get a NEW toliet flapper (like one made by Corky). It helps to have a pair of 9" or 10" Channel Locks to help with the tighning. BUT DO NOT OVER TIGHTEN. Simply follow the directions.
Process of elimination. Good luck.