Roller or hydraulic lifter 360?

I would not be afraid to run the HFT motor; but if the roller is in similar condition at a comparable price, use it.
I have yet to see any roller LA that does not have a long nose cam. If it was a TBI motor (as opposed to the late Lean Burn with an electronic feedback carb- which BTW was only on roller 318s pre '88), you will need to install a fuel pump eccentric with the proper washer/spacer (the eccentric delete washer on the TBI motors is deeper to make up for the missing eccentric, it will not tighten correctly if used with an eccentric). The timing cover will either have a fuel pump block off plate, or the hole for the pump will not be finish machined (easy to remedy with hand tools).
Cylinder wear needs to be checked closely, as you would with a carbureted motor. Remember, these were not a multipoint EFI like the later Magnums; they are a throttle body injection which still makes it a wet flow system, prone to the same cylinder washing as a carb motor only to a bit lesser extent.
Also check the heads closely- roller LA 360s used the 308 heads which, while decent heads, are somewhat susceptible to cracking; although not as common as with Magnum heads. I have only had to deal with one cracked 308 so far.
And on the subject of heads, don't expect to be able to throw just any LA head on a roller block. Non-roller heads have a smaller pushrod hole that needs to be opened up to clear the pushrod angle that occurs with the added height of the roller lifter.
Just a few points to consider.