Now that I've had the car for a year and I've taken care of most of the mechanical needs and lots of other little things, I think the one thing that my car doesn't have to set it out in the crowd is that great shine.

Meguiars makes  a three step system that works well IF you follow the directions. I would be very careful putting a buffer wheel on the car. You can burn the paint and even remove it.

I reckon Meguiars is the best.  My car is black and I only ever polish by hand and does it shine?  Out shines everything else in shows and whenever my club goes on a run.  Only problem with GRP cars is they build up a static attraction which attracts dust.  On a black car.......Oh boy!

Asking for opinions on "the best" car care products is a lot like asking for opinions on what to put on a pizza.  Ten different people can give you ten different answers.  I'll assume a few things here -- that your car is still silver (like the pics would suggest  ), that your car is well cared for, and that your paint is still original, single-stage.  The first step is obviously a good wash!  Remove all the dirt and dust laying on the car from winter storage.  There are many car wash liquids available that people prefer, but for me, ordinary 99.44% pure Ivory soap works fine    If you need to remove layers of old wax or polish before you start, you can use some Dawn dish detergent for a wash.  Second, give the car a once over with a decent claybar and lube (I really endorse the Zaino products and their clay is especially good, but Mothers' and Meguiars and several others also sell claybars and kits) to remove any particles still embedded in the paint surface.  It's really not necessary to clay the whole car, but you'd be surprised at how much leftover dirt the clay will remove!  Next you can address any scratches and swirl marks present in the paint.  Basically, you can either choose to remove them or cover them up.  Removing them is where you would use a good machine polish and your new buffer.  If your paint is single stage and 30+ years old, it may be a little thin in places, so don't get too aggressive.  If they aren't that bad (and lighter colors like silver are very good for hiding imperfections), you can simply try to cover them by laying down a coat of sealant (polish).  There are many synthetic polishes on the market today designed for that purpose.  Multiple coats will only improve the look.  You could also put a coat of carnauba wax over the polish for a "warmer" appearance.  

My '78 Silver Anniversary shines real nice! I first used Mequiar's Gold Class wax, which has been my favorite for a long time. Then I tried Griot's Garage Best of Show Wax and it transformed the car's appearance. It looks like it has clear coat on it.

Griot's stuff isn't the least expensive and you have to order it since it's not store sold, but now I'm sold on their products.

Zen Master Ken warned me about using ANYTHING on a painted surface that contains silicon.  He told me that the silicon will leach through the paint and into the material below (metal, fiberglass, whatever).  Then when it comes time to refinish the surface you have a problem as the silicon doesn't allow the paint to adhere completely with the surface.  (I hope I got that right!  ZMK - please correct me if I mistated the teachings!)

I forgot to mention that my black 71 is clear coated.  Makes a huge difference.

Zaino does make a polish specifically designed for single stage paints, Z-3.