I actually prefer the T-45 to the other types for general knocking around, as it requires the fewest and least valuable resources to repair.
T-51 isn't too far off in that respect however.
20 cores might be a little light from what I remember, although the rate of usage might have been slowed since I last did that quest.
You can also leave the power armor behind and use a Hazmat suit, but since it offers no damage protection, it might be a bit risky given how you'll encounter some dangerous enemies.
