Exactly - why would you want air movement behind the interior walls? All it does is guarantee that if there's one cold spot, instead it makes the whole area behind the insulation a cold spot. Especially the ground level cold will migrate to the basement floor level, spreading the love. Insulation flat against the walls makes sure any cold does not spread beyond where it's cold through the wall.

In Canada, where winters are probably colder at times, the standard now is 2x6 exterior. Or... for basements, a sheet of styrofoam insulation, then insulated 2x4. If you plan to put weight on the walls as others mention, with cupboards, shelving, or tool pegboards- you want the strength of 2x4 on standard 16-inch centers.

The vapour barrier should be on the hot side of the insulation, so inside humidity in winter does not migrate inside the walls to condense. Usually for pink fiberglas insulation, this is plastic sheet on top of the wall, stapled to the studs. Typically, it's "glued" using acoustic sealant so the holes from the stapes are sealed. Electrical outlets 9and cable TV, network, etc.) are on the warm side of the plastic, using tape to seal the wire coming through the plastic. the key is NO AIRHOLES.

(Alternative construction is sprayed in expanding foam, which is then sawed flat level with the studs when it hardens. Since it's sprayed as a liquid and forms a continuous piece, a vapor barrier is unnecessary, it's already airtight.)

Take pictures as you do the work, especially of the walls before sealed from view. Not sure where you are, but here you can do electrical yourself if (a) you know what you are doing and (b) with the supervision of a qualified electrician. (I.e. he/she says "yes, that's up to code".)

Some municipalities require a building permit, especially if you touch electrical or plumbing. I has a relative in the USA, when she sold her house 20 years later, someone somewhere went through the house's building permit history (house inspector?) and claimed the family room behind the garage was never issued a permit to be finished. AFAIK she bought it finished. Then bought and remortgaged when she bought the half it from her (ex)husband, with no hassles. I sold my house in Canada with no such hassles. How persnickety is your municipality?