back spacing

The tire will make a big difference, too. You might want to pick your tire size first, and compare its diameter and tread width with what you have now. Here's a link to a handy calculator, that also lets you play with rim width and offset:
http://www.rims-n-tires.com/rt_specs.jsp

But offhand I'm guessing a 15 x 6 would be no problem, 15 x 7 or up you might need to be right on the money with the backspacing. On Barracudas the critical point is the lower front of the opening, but I don't know about Darts.

Backspacing amount depends on total width. The idea is you want the mounting surface pretty much smack in the middle of the rim, or a little to the outside. So if you have a 7in rim, you want 3.5 to 4in backspacing, or something like that. Hope that helps.

FOR THE FRONTS, If you only run 3.5 or 4" backspacing that will really limit the tire width and height.

You need to run 4.25" or 4.5" backspacing in the front. The 15x7 repro rallyes come with 4.25" commonly. Stock 15x7 mopar rims are 4.25" backspace.

On a 67-69 Dart you can fit a 225/60/15 with 15x7 and 4.25 backspacing in the front. That's about max and you'll need to double check all clearances. If you need some extra room adjust and move the lower fender brace out to move the lower front fender lip out.
215/60/15 would give you more clearance with a 15x7 4.25" backspace rim.