From prototype to printed board - who does the translation from wired proto to circuit board
Very hard long question put that way. Will probably get closed by the kneecappers as 'too broad'. Don't let that put you off - just try to focus in in chunks. 

Note: I have no $ or similar relationship with any persons or companies mentioned herein.

There is a very major implicit assumption that makes a vast difference.  


You say "I basically would like to move from prototype to a board, designed to fit the components that I need (chips and IC on single boards on my prototype),"  


Please note that the following is NOT a complaint or criticism but as a "red flag" (looks reddish anyway):

There is an assumption set that you know what you are doing, that you know that the prototype does what you want, that the board layout is not so critical that it will change the functionality, that you know what actual volume components that you want to use (as opposed to one off prototype ones), that you have costed and sourced these and are not accidentally specifying inappropriate parts based on price or availability or characteristics etc.

It's a reasonable assumption that if you do not know the general nature of the answer to your current question then you are even more unaccustomed to some, much or all of the above. These are part of the role of a design engineer. You are completely welcome to pursue the path of becoming one yourself, but starting on something that needs 100 or 1000 products may be a more expensive and time consuming way of gaining experience in being one. It is quite likely that at this stage you would be wise to acquire the services of a suitable underpaid "hardware design engineer" (maybe qualified by RF/analog/digital lowish speed/digital GHZ ....) with more experience and learn as much as you can by looking over his/her shoulder (as it were). 

BUT, as a guide:

If your circuit is wellishly well defined, not too liable to be affected by PCBerizing, if you know the components that you want to use, have full specifications for them (ratings, physical dimensions, mounting requirements, cleaning cautions, solderability and suitable solder systems ......  .... .. . .
THEN there are people who will lay out PCB designs from what you have got. If they are in the US they will charge from minimum wage (or less) up to too much for you (probably) per hour. People that match the whole range are on this list. I can recommend offlist a man who, if still accepting work of this sort would make as good a job as you'd hope for at a price that is extremely good value by any standards. That's not allowed on list - in due course I can advise if we get that far. People in India or China will often do this work for much less than in the US and it may be very good indeed. Or not. (The man mentioned above is not in the US or India or China ). You can use (I understand) Craiglist and other US and international organisations that I have not had experience of to farm such work out. You will often get MORE than you pay for from such  - but not always.

Once you have a PCB layout you can find manufacturers / assemblers who will make small runs. Some will source components. Some will ask you to provide them. It is usually useful top be able to specify exact source and part number etc. Digikey  is not too bad for this - not as cheap by far as Asia in many cases but very competitive against most other US sources. 

Chinese companies will often provide free design services if volumes are high enough. A 1000 run may be enough for some but not many to get PCB layout, &amp; component sourcing "free". They would source components and any profit they make there would be part of the overall cost.  

If the design is good, the components all fully specified and sourced etc then if 100 are OK the per item price for 1000 would be "somewhat less" than in 100 volume.

I'll stop there and say more if it seems useful based on comments.

You need to explain what you mean by "prototype" (copper etched board, plug in board, ...?), type of circuit (RF, digital, analog, ....?) degree of complexity, approximate functionality, as much as you can.