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One more note:

. . . I would get a _round-point_ razor, not a _square-point_ razor.

The round-point is less likely to gouge skin, in the hands of a beginner. It's possible to "mute" the tip...

FWIW:

$100 is plenty for a vintage straight razor and a strop. Don't be tempted by eBay -- too much risk. New _decent_ razors start at about $80, so they're out of range for you.

There should...