Unfortunately, no, you can't disable the rats nest for individual nets. This was discussed in the thread Turn off GND airwires about a year ago. Some Forum members suggested workarounds that accomplished a similar effect, but with the possibility of significant errors if you didn't back-out of the workarounds after they had served their purpose. The thread Local ratsnest - Do you use it? also has some suggestions.
From my perspective, component placement is by far the most difficult aspect of board layout. It challenges your ingenuity and creativity. In the designs I've done, I can get along quite well without a real auto-router, but I can imagine saving man-weeks of work if I had a true auto-placement tool.
Niels ( @trcwm ) gave some good advice! I don't have an standard system for component placement, but I have observed a few things that seem to help the process, and a few patterns that worked in some specific situations.
Of course, if you have a specific board outline - it must fit inside a particular enclosure, with defined mounting holes, etc - that must be your starting point. Even if the outline is rather loose - e.g., "keep it under 4" X 6" if you can" - I'd start with at least a tentative placement of connectors, switches, pots, battery holders, front-panel LED's, etc. Sometimes this cascades into defining positions for associated amplifier stages, LED drivers, battery charger circuits, etc.
In some introductory texts you find the advice to place components in roughly the same relative positions as their symbols on the schematic. That sometimes works as a starting point, especially if you have put some effort into drafting the schematic by eliminating crossover lines. It tends to ignore the problem of those pesky power nets and associated decoupling components. Oh, and the fact that package pinouts don't follow the relative positions of connections to schematic symbols.
The first thing I usually do after importing a netlist is locate the component pairs (if any) that are electrically in series or parallel, and position them adjacent to each other. This reduces the two components to a single item, and reduces the ratsnest clutter by a little bit.
In a similar way I sometimes work out the layout for a portion of the circuit - an amplifier stage, power management section, etc - off to one side and then move it into location on the board itself. This works best when there are only one or two inputs or outputs for the subcircuit. KiCAD's ability to do a "block move" (with components visible while moving) lets you try out the tentative layout into the space you have in mind for it.
Combining several components into a single package - dual transistors, opamps, etc - seems like a way to reduce PCB real estate until you have to make connections to all of those parts. I stay away from quad opamps, and I recall a design that used two, single opamps rather than a dual because of layout considerations. Fortunately, the pinout of dual opamps is generally - but not universally - standardized, so once you have a component placement that works for one opamp circuit there's a good chance you can replicate it for another.
Good luck with your project, and keep us updated on your progress.