What other parts might need replacing if I replace an old freewheel gear set for a modern freehub cassette? I currently have a pre 1970s 10 speed Claud Butler. Perhaps back then men were real men but there is no climbing gear. Since I mostly do touring this is a bit of a problem. Finding a new freewheel gear set with a climbing gear has been tricky due to their rarity in shops. One suggestion from a salesman was to change out the old freewheel gear set to a newer cassette freehub gear set.

When changing to Shimano's new cassette freehub (which from what I gathered from the jargon in the shop I visited was the new standard) I know that the wheel will need replacing (right?). That isn't perhaps so much of a concern since I am missing a spoke and should perhaps replace that regardless.

I am concerned that this upgrade might spiral out of control in terms of labour and cost. What factors about the upgrade do I need to consider to minimise the amount of other components that I need to change? For example, in a typical upgrade like this would I also be expected to buy a suitable new rear derailleur and chain? Will the swap affect my chain ring and front derailleur? 

Ultimately, is it possible to buy components that will be reasonably compatible with my old components, and how do I identify compatible components?
You probably have the right drop out width.
Unless it has down tube shifters you have cable routing.
The chain size must match (e.g. cassette number of gears) and chain ring width.
Your existing chain rings are probably too wide.
But I think you would be better off finding a newer used bike with the stuff you want. 

If you stay with the same number of gears and get different gearing (number of teeth) you can get better climbing.