but my 1st goal is to get the bike up and running correctly before I make any modifications!
That is probably the best plan that I have heard from a 1st time owner yet!!
Start out by taking pics of every part of the bike to build yourself a photo diary. When the time comes that you have trouble remembering how a part was installed, or a cable was attached. You will be able to look at the pics to help figure it out.
As you have already gotten a lot of good info. I will focus a bit on some of the trouble spots.
First off. The electrical system on the bike should be gone over completely to make sure that there are no problems with loose, or corroded connections. Any bike that has been sitting long enough for the tires to become questionable has sat long enough for the electrical connections to become questionable also.
The charging system is one of the biggest trouble spots on the 650. This is usually cause by the harness connections becoming loose, dirty, and corroded. The most common result is that the rotor goes bad, and takes the reg/rec with it. Make sure you clean out the carbon dust buildup from the alternator, and check the parts for correct readings.
The problem with the carbs sounds more like the slow/pilot circuit is dirty. This will be the pressed in slow jet on the CV carb, and must be taken out to be cleaned properly. There is a method for removing that slow jet posted here somewhere. I am unable to locate it at the moment. It involves using a screw, and nut to pull the jet up out of the hole that it is recessed in.
When you have the new tires installed. Have the spokes check for proper tightness also.
One final thought. The cruiser styling of the 650 is tough to work with to get the cafe image from. The frame was changed in the '80 models to allow the drop in the seat. This makes it hard to get that clean, straight line of the tank and seat for the cafe. You might want to look into it more before getting to far involved.