Help rebuilding 1970s bike - rear wheels

1970's frame is going to be 5 or 6 speed - if you measure the width of the rear frame drop out it'll be 120mm or 126mm. All wheels of that era use a screw-on freewheel, not a cassette - you can squeeze a 7 speed freewheel on some 126mm frames. Back in the day, there was no worries about indexing, you can pretty well mix'n'match parts to your heart's content - it was only in the 1980s did the likes of Shimano started tinkering with 'groupsets'.
If you go onto the Retrobike forum, you'll probably find suitable advise and parts for reasonable money rather than trying to make it work with modern parts.

With friction shifters you should be fine with anything up to 8- or 9-speed I would have thought, as long as the derailleur cage is long enough for the gear range (the number of sprockets shouldn't matter). It's more important to match the chain to the number of sprockets - a 6-speed chain will be too wide for the spacing on a 10-speed cassette.

One other thing to look out for is that you may need to spring the rear dropouts open a bit to get a modern wheel in - if I remember rightly modern frames built for cassette hubs typically have the dropouts spaced at 130mm, while yours is probably 126mm. Sheldon Brown as ever has a bit on this too. It's 2mm either side so up to you really whether you want to bother bending the frame...

Never done it myself but I can't see how the make of friction shifters would matter. After all you're just tightening the cable until the chain moves onto the next sprocket.

My understanding of rear mechs (mainly learned from the great Sheldon B's website) is that they're not specific to the number of gears but they are limited to the chain dimension. I've certainly used 7 speed mechs on 8 speed drivechains and vice versa.

Basically, the shifter and cassette need to be designed for each other. If it's a 5-speed shifter you'll need a 5-speed cassette of the same brand so that the spacing is right. However, Suntour freewheels are unlikely to be widely available. Your best bet is probably to find a freewheel/cassette and shifters of the same brand and number of speeds, and attach that to a wheel of your choosing. This is where my knowledge gets foggy - I don't know if Shimano shifters are compatible with a Suntour rear mech. The geometry may be different (so it will only move half as far as it should). If so, you may need to replace the rear mech.

As ever with this type of project, Sheldon Brown's website is extremely helpful; www.sheldonbrown.com The 'old bikes' section is good, as is the 'gears and drivetrain'.