[Accelo]

The 1997 4L60E will not have the hole on top of the bell-housing and requires a different flex plate to adapt to the LS motors.
Because they are 3/4" shorter than the newer ones. The bell-housing area was extended to accommodate a larger torque converter.
I suggest getting a 2001 or newer 4l60 or 4L65. The newer transmissions have the larger torque converters (300mm) and are a direct fit to the LS engine family.
Well most of them. A few, LS motors, had longer crankshafts and you want to avoid those.

The bad news, it the newer 4L60E and variants do not have provisions for a analog speedometer.
You have to add it go go to a digital dash that uses the existing output signal for the transmission.
You can't retro fit the "Older style" tail shaft as they have 4 attaching bolts and the newer transmissions have 6.

You will likely run into the same flex-plate issues on a 4L80E. Acquire one that came behind a LS.
Even the 4L80E cores are expensive especially compared to the 4L60E sister transmissions.
Getting a "matched set" will reduce your stress for sure.
Cheers