Welcome to the wacky world of sidecars! I have no idea as to why you need 3 wheels, but what ever the reason, it is a great thing that you will be able to use a sidecar to get out and enjoy the ride.
If you lowered suspension didn't cause problems for you before, it surely shouldn't with the sidecar attached. As long as Jay knows the ride height of bike the subframe & mounts he makes for you should be able to handle any adjustments.
Your suspension may be pretty good as is, but I have no idea as to what your existing set up is. Slower dampening with higher viscosity oil may help and it is one thing that you could "play" with.
With the added weight, a wee bit lowered geared is not a bad thing at all. Sorry I don't know anything about your bike, or what size chain it uses, but a side car will add stress to the drive train, so I would go with the heaviest duty available (that you can fit in your budget).
Tires on sidecars are always an issue as sidecar rigs simply don't turn like a bike. You will scrub off the center and square off just about any tire you put on it much much faster than you would like. Those of us with big 1200GSA rigs opt for tire car conversions, esp. for the rear. Claude or Jay should be able to point to tire solutions. The PSI should be close to the same if not a bit more.
"I couldn't wait for success, so I went ahead without it."