once the OP has enough posts it would be good to see pics of the bike, lots of pic to under stand what the frame is and the components
an older steel bike for 250 could a schwinn varsity or a de rosa
a decent frame may be worth upgrading, but almost always is less expensive to get a whole bike (that said I really like the combo of high end older frame with modern gear)
as noted by others the single most cost effective upgrade is to get good tires, but if current bike has 27 in rims, tire choice is limited
IMHO, it is not one single thing like frame weight that makes a difference but the combination of frame, components, position on the the bike in total
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