Soldering components to brass pins stuck in shellac or paraffin wax impregnated balsawood (or other low density kiln dried softwood you can set pins in with a pin punch or just a pair of pliers) was the origin of the electronics term 'breadboarding', from literally building a circuit on the significant other's wooden breadboard! Its still viable for point to point wired circuits using leaded components at frequencies below roughly the middle of the HF band. Panels for controls etc. can simply be screwed to one edge of the board. It can also look pretty good (1920's retro-tech) if you take care to make an aesthetic layout, use hardwood, rout and fine sand a molded profile on the edges, highly polish the shellac before assembly, and pre-drill the pin holes under-size so you don't mar the harder wood setting the pins.
If you need to work at a higher frequency go Manhatten Island which with careful layout is good up to the low UHF band. Its also *MUCH* better suited to SMD prototyping, (dead bug or on small breakout boards) and even if you don't want to use SMD for the bulk of the circuit, its still worth using SMD ceramic caps for sub-uF decoupling - just tombstone them directly on the ground plane and use the top end as a circuit node. 0805 or larger 100Meg 10% SMD resistors make quick, good and cheap low capacitance standoffs for 'air wiring' parts of the circuit where you need to minimise capacitance to the ground plane. If you need low leakage standoffs, then its expensive pins in Teflon bushes in drilled holes.
Above the low UHF band, the layout *is* the circuit reactive components, so you need to cut carefully designed and dimensioned striplines etc. on double sided specialist low loss PCB material, and 'fence' round the edges of ground islands with copper rivet vias to stitch them down to the ground plane, then edge solder the assembled boards into screening cans. Its not too bad if you've got a good CNC mill with a precision high speed spindle and a supply of small conical carbide cutters, and small carbide drill bits, and can go straight from CAD to PCB ready to copper rivet the via fences (and don't mind the effort containing the abrasive PCB dust so it doesn't get into the mill's ways), but is a royal PITA if you are using hand tools.
Put the breadboard (of whatever construction technique) in a biscuit tin (or sweets tin - Altoids is the classic) and spot solder the lid on a couple of points on each side (or use PC case panel grounding clips) for screening. You can also build screening boxes by tin-smithing from bent and soldered tinplate. Another method is using copper clad PCB, with the seams soldered. Double sided PCB is stronger with a slightly oversize baseplate and end walls, with all seams soldered both sides.