What size battery is recommended? on 2001 Chevrolet Silverado 1500 HD

I see a size 78 on the old battery, but not certain if other sizes would work as well.

I would recommend you stay with the Group 78 battery. There are other sizes that would "fit"...such as a Group 75, or a Group 70...basically most of the Group 7(?) will fit. But, keep in mind, the Group 78 battery will have more CCA (Cold Cranking Amps) than the other sizes. So, to be on the safe side, I would recommend staying with the Group 78. Here is a link I found that might help you determine what size (length, width, height) is you decide you want something other than stock.

Good luck