Hey Bus Driver
Welcome to the forum, and for having just bought Harley's finest vintage!
The CV carb is a good one, but I do recommend you to get a rebuild kit:
Although the scoot has seen very little road mileage, it's been sitting for a long time and rubber parts are probably dried out. You need to open up the carb completely for cleaning, so you should replace the diaphragm for the accelerator pump, new O-ring for the float bowl, and a new O-ring for the accelerator nozzle. Oh, and new gasket for the carb to air box as well.
With the kit (I've used various aftermarket ones mostly with success...) you'll also get a new float valve, which could be useful. There seems to be some slight variations with these and during my last rebuild I had to swap back to the old valve as I could not get the new one to close properly - it was ever so slightly longer than the old one.
You need to set the level of your float correctly - use a piece of clear tubing connected to the overflow, tape it up along the carb so that you can see the level inside, should be to just below the bowl flange. Sometimes the valve sticks probably caused by dirt getting stuck on the valve seat causing your leakage (if it leaks you could try to run the carb dry, i.e. close the petcock and let the bike idle until it dies).
The diaphragm for the CV slide (under the top cover) is tricky to get back sometimes - it seems to grow when taken out. IF this is your first Cv rebuild you should not open it unless you need to. This means; clean out the jets and passages carefully, put it together with new rubber stuff, set the level and see how it behaves. IF you have a torn diaphragm the slide will not operate well, and you will notice.
As for the tank, personally I'm sceptical to the various tank linings as they may do more damage than good unless the tank is absolutely spotless inside. A good clean-out should be sufficient. I've never used any lining, but taken care to preserve the inside with motor oil during the long winter months. I take about a litre - quart - or so of oil & gas mix, and turn the tank upside-down to make sure all surfaces are covered (yes, I do take off the tank first
.