" Any advise? "
The EM theremin does not have a PCB - and I dont think the original prototyping board is available anymore.. So you are really going to need to plan the layout first. My advice here is to get some PCB layout software, something free like DesignSpark, so that you can plot a basic layout for 0.1" PAD BOARD (NOT Strip board or Matrix board).
My advise is also that you split the design over several small boards - You want each oscillator on a seperate board, and the mixer and VCA/Audio stuff on one board IMO.
Read everything you can on both the EM and EW theremins, enter the schematics into the schematic editor of your PCB design software, you are then ready to do the layout.. Lay out for two layers, but make any tracks on the upper layer straight - this way you can wire link these. Keep all your tracks, components etc TIGHTLY on an 0.1" grid - this way you can simply put the components down on the pad board where they are supposed to go, and do point-to-point wiring on the other side, soldering the wire to pads and using the pads to fix the wiring at bends.
Using a schematic + PCB editor, you will be warned if the rule checker sees that you have made a layout error, left tracks unconnected, or have not fitted all the components.
IMO, if you dont do the above and just dive in with a soldering iron trying to copy the EM design, well, you dont have a snowballs hope in hell..
If you use schematic and PCB editor, you should be able to copy the component placements from the EM article as a guide, and the PCB editor will help greatly as you will see "ratsnesting" showing the required connection between components.
My advice would be that this is not a starting project - I would echo Chobbs advice loudly - But hey, luck sometimes favors the foolhardy...
PS - When you enter your schematic/s, keep the component references the same as the EM if you are copying that, or the EW if you are copying that.. This way you will be able to cross reference against the original parts when you do your layout.
Also - Make all connections to components on the lower (solder side) layer - The PCB layout editor will place "vias" when you go from lower to upper layers - but these will not exist when you build your board - Every connection to the upper layer, and every "track" on the upper layer will need to be hand wired ( - so dont take an upper track to a component pin directly, it MUST go back down to the lower layer before it connects to a pin.. there are no plated-through holes with pad boards) this is why they need to be straight - if they are not straight, or if they come too close to a component lead, these wires will need to be insulated.
Oh - one last thing.. Use good quality turned pin sockets for all ICs, and as you havent soldered before, I would advise you to buy some socket strips you can cut up to make sockets for your transistors and diodes as well - they dont like getting their legs cooked for too long! - And I would buy a load of cheap components (resistors or whatever) and a spare board, and practice soldering these, and wires, onto this board.. then practice unsoldering them and removing them, and cleaning the board (you will need a solder sucker and some solder wick) then re-mounting them and re-soldering - Do this until the board is a complete wreck!
Also - Use tin lead solder, not the new RoHS lead free rubbish! - The new solder doesnt flow (or wet) as well, is more brittle, has a higher melting temperature, and is quite horrible!