when i fixed up my mixte, the first thing i got rid of were those extremely heavy steel wheels. The bike shop put on a used pair of "alloy" wheels and the bike was suddenly a lot lighter. Plus wet steel wheels are scary to stop.
when my bike was all done being fixed up with mostly used parts, the bike shop made a little money and i had a bargain bike.

good luck! i hope you have a bike shop who will operate that way.