The set comes with a Z-500, which has no notable issues running traditional Lionel per se. I have used one on a simple loop to run every era and style of trains for circa 20 years. One caveat however:
It is rated to supply 1A less "power" than the CW-80, which may or may not become an issue depending upon which locomotives and cars you own. That is, the Z-500 (50W, 4A) might not be enough to effectively operate traditionally powered ("pulmor" (non can-motor)) Lionel especially if combined with multiple passenger cars with incandescent lamps and/or multiple motors. For example, the Z-500 can generally handle one two-motored (2343) F3 pulling freight, or a single motored steam engine (2037) pulling 4 lit passenger cars, but not necessarily a F3 pulling 4 lit passenger cars.
Note that the CW-80 (80W, 5A) actually has the same problem, but the extra 1A makes it slightly less an issue. You would notice the light blink and power "foldback" activate as the limit approaches. If this already occurs with your current trains, then switching to the Z-500 is not ideal.