If the car is mint I would not change the rims, but keep the original wheels and trim rings/hub caps. And if you do change the wheel size chances are your speedometer will not be accurate. You can get 185/80 R13 WW tires from Maxxis tires. The tires are pretty decent riding and handling, although it seems like they are a little rough for the first mile or so. But that's on a car that is not a daily driver and sits for a couple of weeks at a time. This size tire fills the wheel wells nicely and is the closest diameter to the original bias ply tires. I got five tires for $499 with shipping a little over a year ago from Universal Vintage Tire. Here's Maxxis' web site. They have an alert about this size tire, which you can order direct from them. Maxxis Tires
I would just buy tires and use the money you save by not changing rims/trims to pay for some of the other things that will definitely need to be done.