"Okay, so I will scrap my protoboard circuit, and go with your version, Thierry. I've never used it, but I've ordered some matrix board and all the components that are on your design, so it will be a great learning experience, hopefully I will do it right, but I've got some solder wick if I make mistakes (its my first time), and I'll post my results either on here or on your thread :)" - pauliudean
That schematic looks rather dubious, but I think you can continue to use a protoboard for your Theremin circuit prototyping. If you are careful with layout it will still probably influence things somewhat, but is isn't necessarily a death sentence at these frequencies, and protoboards are enormously convenient. They can have high capacitance between adjacent rows, and also capacitance to whatever they are sitting on or mounted on. The one I use for oscillators is double-stick taped to a piece of plexiglas, but wood or almost anything else non-conductive would do, as would simple legs to give it a bit of height.
Your wiring looks clean but I would aim for being less "neat" and more direct point-to-point with wires utilizing the third dimension (up in the air) to avoid packing them too closely together or running them near the protoboard surface. Of it course it depends on what a particular wire is doing, most are non-critical and can be placed / routed however you feel. Getting too neat is IMO generally a waste of time as you're trying stuff out not making a finished product. Don't forget to decouple here and there with capacitors from supply to ground and small value series resistors feeding them. Really strong undesired interaction between unrelated circuitry might need a choke.
Active devices that have significant delay at the operating frequency should be avoided as they will almost certainly be a major cause of thermal drift, and the delay can throw things off of the natural resonance point giving you a smaller voltage swing at the antenna. Op amps and the like aren't well suited to >300kHz operation as oscillators. You want to employ one or two transistors here, or fast CMOS digital logic (in either analog or digital mode).
Series LC tank oscillators tend to be sensitive to inductor self-capacitance, but I currently have one running at 2.5MHz on a protoboard (which is 5 to 10 times higher frequency than what you normally find in a Theremin). One of the tricks is to connect the antenna end of the inductor directly to the antenna in the air with a clip rather than employing protoboard connectivity for this. Parallel tank oscillators like Thierry's or livio's are more forgiving in this regard.