Very nice!

You probably should have kept the stem, but judging by the other rust I see, let's not belabor that issue. This bike could certainly be restored to a lovely rider.

Looks like the paint is pretty far gone; you will probably have to repaint. You can get the correct decals from H Lloyds Cycles.

Your chain set is a Wiliams, and very nice; I would try to clean that up and keep it. The brakes are the deluxe version of Weinmann Centerpull brakes, made about 1960; very nice. You can probably replace the rusted steel bits with the equivalent ones from newer Weinmann or Dia-Compe brakes.

The derailleurs are nothing special; you might want to replace those.

I don't know about the existing wheel; you might want to find a matched pair and not worry about the old one. But check to see if 700c wheels will fit; your existing wheel is 27" while 700c (the modern standard) are a few mm smaller. The question is, whether the brakes will reach the smaller size wheel. If so, I would definitely get 700c wheels. If the brakes won't reach, I'd stay with 27".