Or better yet, a used modern bike to avoid instant depreciation.

I'll add that the 'upgrade' avenue is one to take if you're interested in tinkering. Lots of regulars on C&V enjoy collecting lots of bikes and adding to our parts bins, so we have more flexibility when it comes to upgrading something we think is worthy. This takes time and labor, however. One reason to upgrade a classic or vintage frame to modern components is because you know the frame is right for you. It's not economical or sensible to do this to a random frame that you do not have experience with or which does not come highly recommended.

On the other hand, you can find a reasonably priced vintage bike in the $150-$250 range (some completely overhauled for you) that will get you into riding inexpensively. You just have to spend some time researching so you know what to look for, or make friends with someone here who does!