I’m always a proponent of making sure the engine is sound mechanically for the simple reason that over the years I’ve seen so many cars that have had everything in the parts inventory thrown at them without curing the problem. So a compression test is always mandatory with a performance problem.
If you want to make things a bit easier before a compression test I might suggest the use of a vacuum gauge. Those can be connected in seconds and will tell you instantly whether or not to proceed with a compression test.
The vacuum gauge (they’re cheap from Harbor Freight or whatever; not so cheap from Snap-On) is connected to an intake manifold vacuum source and the engine allowed to idle. An engine with good compression will usually show around 20" of vacuum with a rock steady gauge needle.