Welcome to the wonderful, wide, wild world of Classic Mustangs!!!
I'm sure you know that lots and lots of things can cause a "loose" feel in the steering - worn parts (ball joints, tie rod ends), improperly torqued wheel bearings, and a worn steering box. It's also possible that the alignment could be off, giving a loose feel when driving.
First you need to find out if there is play in any of the suspension components mentioned above and fix those. If you still have play in the wheel at rest then perhaps the steering box is worn.
A rack and pinion system, if new and if properly installed, can eliminate that but they require fairly significant changes to your vehicle to make them work and they are quite expensive without the additional changes needed to install one and make it work.
There are people that rebuild the stock steering boxes (http://www.stangerssite.com/
is one that I know to have a good reputation but he is overwhelmed and it will take time to get yours back). You can buy replacement boxes from several of the Mustang aftermarket suppliers (National Parts Depot, etc.) and there are "new" aftermarket replacements that are also available. I bought a Flaming River replacement box for mine many years ago and it's still holding up well. Personally, I'd suggest a stock type replacement simply because it's much simpler to put in (although it won't be "easy") and because it requires no change to your stock vehicle, it will be much less expensive and it will perform as well as a rack and pinion.