First thing to realize, is that you don't have a bike, you have a rig - they handle totally differently. If you do not have experience with a side car, or hack as they are popularly known, get as much information on their behavior as you can. There is a book that you should try find: Driving a Sidecar Outfit, by David L. Hough. I cannot stress enough the value of this book - it is a life saver.
Things to be aware of with the hack - you need to turn the handlebar to turn, and it needs you to move your body in the direction of the turn. This body movement is to keep all three wheels on the road. When you speed up, the hack will hold you back - if you are in the US, the hack is on the right, and you will veer to the right whilst accelerating - not much, but some. When you slow down, the hack will speed you up, so you will veer to the left, not much, but some.
In extreme braking, if the front wheel locks, you will veer violently to the left, right into the path of oncoming traffic, so you need to think ahead at least 500 yards. Anticipation is the tool you need to use.
These things are the negative side of sidecars - Turning towards the hack (right in the US) may cause the hack wheel to lift off the ground - this is only alarming, if you don't know it happens. I practice lifting that wheel often - it is called 'flying the chair' and if you can do it at will, you can control the rig much better than you could. Crashes involving sidecar rigs happen usually when turning. Left turns can lift the rear wheel of the bike, right turns can lift the hack wheel - if you ain't expecting it, it will cause problems. Severe braking can cause the rig to swerve. Of all of the sidecar crashes I know about, 80% were front wheel skid, veer left deals.The cozy is different in as much as it does not come with a sidecar brake - I ride a Ural as primary bike rig, and it has a sidecar brake. This being said, I am intending to buy a cozy, for my Bullet in the new year, so the lack of a brake on the hack wheel is not too much of a problem.
Positive aspects of the sidecar... You don't fall over at stop lights; you can ride all year, (my Ural is 2wd, so I can drive any weather too) You can carry way more in the hack than a bike can carry. You will experience an amazing amount of Delay Factor - people ask about Royal Enfields all the time - add a hack, and they will ask more often. You become more visible, making it a safer option.
The best thing you could do for yourself, would be to find a sidecar rider course, and go there.