It depends what you are happy with. To do it right you are looking at a bit more than 200 dollars.
I would guesstimate 5000 to 6000 to make a convincing Newman. A Valjoux 72 is going to cost 1000-1500 before conversion parts are added and there isn't really a great substitute available. For a case, other than genuine, a Phong/Jenson is about 1400 IIRC, DW or Tonnywatches a bit less with a correspondingly less accurate design. Dial, well again Tonnywatches is around 400, good vietmanese a thousand plus or best of all a genuine one, but probably not a true Newman.
Daytonas are not easy. I am sorry to welcome you to the forum with such bad news. On the up side virtually any other Rolex is easier and cheaper. As cheap as 120 Dollars for a reasonable 5513. Ideally you would want a crown, dial and crystal upgrade on that, so maybe view it as a starter kit. This hobby is addictive.