so,
i have a 10 speed Schwinn varsity (1974 i believe) that i really like, but i need to change the wheels, dérailleur, maybe the cassette, and the brakes.

i found some pretty cheap 27" by 1 1/4 alloy wheels but they are for 7 speed
i don't know which dérailleur to get
i have found some shimano 5speed casettes
and for breaks im assuming any modern shimano brakes should work

does it matter if i get 7speed wheels and use a 5speed cassette?
im new to working on any bikes other than when i was a kid but i have a good ability to use tools and all that.

any suggestions on which equipment i should use for this job? wheels, brakes derrailleur?
or is it hard/safe to space the frame and just go with a 7 speed?

im pretty much in the dark with most of this stuff

any help is much appreciated

What shape is the bike in right now?

I need to see some pictures.

i dont have a camera right now.
its in good shape just that the dérailleur is messed up, its beat and bent and does not shift well, ive had it working for a while but not very good at all.
i just want alloy wheels to be lighter and stop better
ive tried adjusting the brakes all the time but they just dont clamp down ever, they dont really slow you down much, but it could just be the surface of the rim is what i have been told, so that will be last.

i really just want wheels and a dérailleur

but i cant find 27 1 1/4 5speed wheels anywhere.
im ok with a new style dérailleur but i dont know which one would fit.
would a 6/7 speed one work for a 5 speed cassette?

here is the wheels i want to buy
https://www.amazon.com/exec/obidos/tg...8MWQU&v=glance

and this is what i was thinking for the dérailleur
https://www.amazon.com/exec/obidos/tg...28WSA&v=glance

You could buy another complete old Varsity ( usually 50 bucks or less) with all working components for much less money than replacing the parts you've listed. You could then swap the parts onto your bike, or simply find one as nice if not nicer than yours and replace the whole bike. In other words, a Varsity usually isn't worth putting much money into unless you are realy attached to it. You can upgrade it with lighter components but it will still be a tank. If it were me, I'd look for a fillet-brazed cro-mo model like a SuperSport that would be more worthy of investing money into.

THe 7 speed hub should be ok with the derailler but you might not be able to reach all the gears. you might have to spread the frame a little. there's plenty about that on other threads and at sheldon brown's sight.