All of these questions have answers that are based on very subjective and personal choices.
Yes, you should look at buy a frame that fits, if this one doesn't fit.
No, I wouldn't build an old frame with new (even new old stock) parts, since the value of the complete build will be far less, generally, than you will spend on the parts to build it, and many of the parts will need to be replaced if you pick a new frame to rebuild everything on later.
Are you doing this as a learning project? If so, then the education might offset the extra cost involved. If you just want a fixie, fixies are cheap. I'll pretty much guarantee you can buy a better fixie than you can build, for around the same cost.
All of these are things you have to weigh the value of for you personally. I wouldn't do it. But then, I know that because I've done it. So how should I tell you not to do it?
Do it or don't, as long as you are aware it isn't the cost effective route, but it might be the fun, DIY route for you... If so, Enjoy it.