One of these should do it
Properly cleaned and lubed, your unit can track without problems between 3 and 7 grams. This means you should go with the cartridge these people recommend, not necessarily the exact same one in your V-M right now - V-M was keeping up with advances in technology in that era and your exact same model could very easily have had a much better sounding (and easier on your records) cartridge built into it. You aren't violating purity or any such thing by upgrading here - my grandparent's 1959 VM console was updated twice over it's very long life (the second time from me to a magnetic cartridge specifically built for V-M changers. That, of course, would be a step too far. Shure was wonderfully creative in those days and enormously helpful to little kids who wrote them. Today, you're lucky to get someone on the phone who speaks English...)
Given the relatively long life of diamond styli and the shrinking inventories, best buy an extra stylus while you're at it...you never know.
That speaker problem, if you will forgive me, I have a slightly different opinion to many here.
Your unit used a very common approach (used nearly universally in 5.1 surround sound). There is only one woofer, each channel has its own mid-range and tweeter. Perfectly solid physics because our ears can't locate the lowest frequencies' points of origin.
This means the costs of replacing the mid-range and tweeters is considerably less than if two woofers were involved. I strongly urge you to re-new the crossovers (I think you are looking at three capacitors in total here) and replace all four of these speaker with sold technology from today. The vacuum tube amp in this unit is probably being made and solid in more or less the same configuration for thousands of dollars as "audiophile". But speakers of that era can't touch what was available even at the end of the 1960's, much less today.
(Magnavox is a big exception here and their speakers' weaknesses and strengths were part of the entire system.)
