With a BH600 you should have a versatile machine.
I have had a BH600 lookalike (not a Craftsman) with a VFD, from new, 15 years ago, and am happy with it. It does not claim to be a Tool Room lathe, but is quite accurate enough for my work. (It will turn and bore mating pieces that will "pop" when pulled apart, or "bounce" if oiled and pushed together 
.
It is not perfect, but nothing is; and a little attention will remove some of the smaller silly annoyances.
My only complaints, on my lathe, were: A ball oiler sited where it was inaccessible, and a belt tensioning lever with too shallow a dimple in the shaft, which caused belt slip, until the cause was spotted and rectified. The Bolt for clamping the Fixed Steady needed to be made captive. A simple, but useful improvement.
DO: replace the 5 mm roll pins in the power drive shaft and the Leadscrew, with brass shear pins (5 mm OD, 2.5 mm drilled through ). It may save you having to replace the pinion shaft and damage to the Rack if you do what I did, and run the Saddle into the Headstock! (Tightening the capscrews on the worm housing behind the Apron is not impossible, but VERY awkward and time consuming ).
Part of this work, while the Apron was off, was to turn up a nylon bung to close off a hole so as to raise the oil level.
I did make up a 80T gear to replace the 40T on the input to the Norton box, but this entailed destroying the knob to resite the closure for the gear cover. This enabled the feed rate to be halved.
PM me if you want further details.
Enjoy yourself!
Howard