How good do you need it to be? If you are aiming for State of the Art performance, maybe you would be wasting your time. If you just want to enjoy some vinyl, it would probably be fine. You can buy a lot of music with the money you would spend to get something more "current". Even then your Versa-Kit would probably show up a lot of newer, pricier gear.
Since you brought it up though, I'll toss out a related question: I too have the ca. '92 Versa-Kit multipurpose board, currently configured as a line buffer, and am thinking of rebuilding it in the headphone amp configuration. I was wondering if there is a better op amp choice available now than the AD843's which are in there presently. The improvements over the years, I suspect, have been mainly in the active circuitry which is entirely in the opamp. So could I (or you) get more "modern" performance by "chip rolling"?
Also, Frank was talking not too long ago of reintroducing a multipurpose board that would essentially be the equivalent of a new Versa-Kit, but I haven't heard anything about it for awhile. Wonder if that's still in the works?
I'm sure AVA would have the answers to all these questions...