It is quite a mystery as to what your circuit is supposed to be showing.
You have a very steep learning curve ahead of you if you want to go down this route of building an H-bridge. The 'quickest' way might be to go pull data sheets for H-bridge drivers - manufacturers of these put in some good information into their data sheets, obviously aiming to be as practically helpful as possible to sell their parts. If these datasheets fail to inform you because they are beyond your current level of learning, then it's difficult to make a suggestion as to how you are best placed to get to that point.
Some drivers make it so simple it
is almost as easy as it looks! IR2453 [
http://www.farnell.com/datasheets/48102.pdf ] has in built oscillator, bootstrapping
and dead-time. (If you do not understand bootstrapping and dead-time, and the difference between inverting and non-inverting drivers, then it is still better you find out before using a driver like this.)
A problem you do not yet appear to know you have is that without filtering on your mains rectifier stage you will have an output which follows the mains frequency.
