I just got a 68 convertible, I think it has H70s on the front and 60 series on the back. What size (in todays sizes) do I need to go with???

 

Your car didn't come from the factory with 60 series tires. Not that it matters much, mine didn't come with 50's either! The factory 15" tires (which only came on the Z/28) were E70's, so you're up-sized by a couple. If you like the sizes you have, all you have to do is convert them to current day metric sizes. For instance, H70 15's (you didn't say if you have 14 or 15 btw) are equivalent to 225/70 R15.
Here's a conversion chart: Tire Size Helper