You want to ride with traffic. Everywhere I know of riding against traffic is not only unsafe but illegal.
While there is some dispute on exctly where to ride I do not know of anyone who advocates moving in and out of parked cars.
One hint rarely mentioned is try to find streets that do not go through 'all the way' It is amazing how much calmer the traffic is on a street that 'only' goes 5 or 6 miles.
Ask at local bike shops abotu routes and also about local clubs. Most bike shops are happy to halp you find clubs to ride with since that means you ride more and at least waer things out if not eventually beginning to lust after a better bike. Most shops near me have a little place set aside with hand outs from clubs and/or local governemnt with cycling information.
Back to with or against. If you go 10 mph and the cars go 30 then you are closing with the cars at 20 mph if you are going with the cars and 40 if riding against traffic. Riding the wrong way the closing speed is twice as fast.
Read some of the sticky threads in this forum, there is lots of good information, but remember things do vary a lot from place to place.
Oh final hint early (e.g. before 10 or 11 am) on the weekends is often a nice time to ride. Rush hour is often the worst.