Good post #14, to remember Malaya, Portugese Africa, Rhodesia, &c.

I'm affraid this look back tends to be too romantic, boy-scout and action movie type romantic.

And when ordered to build a unit, I have to ask for what mission. Rural? Urban? The real deal, or "hearts and minds" stuff?

Generally, these days I would go irregular. Recruiting people of suitable and theatre-compatible racial/tribal/cultural background, either in the theatre itself, or from the huge pool of economic and political refugees that is available in the West. Exploiting racial, tribal and social conflicts. Led by visually compatible members of special forces with special education.
Pose as business men, workers, tourists, local security, the new gang in town, &c.

The whole outfit organised flat. Trooper - Section Leader - Company Leader. No status games and a minimum of "Sirs". No real uniforms, blending in with locals.
The size of the section maybe 8 men (not different from a regular squad), the company maybe 15 to 20 sections. But the section here is more important, the company more a paper unit. The sections would avoid "coming home" when in theatre.

Logistics support by buying stuff, other stuff by FedEx or DHL. (I'm not joking, FedEx is in Iraq since 2003. A lot of stuff can be delivered commercially - very low profile).
In more rural areas GPS-parachutes.
For mobility take a taxi, or buy something.

Two huge advantages a Western COIN unit has are ISR and precision stand-off fire power (which is important in case a hundred Pashtuns decide to have your scalp).
That makes the question of weapons a little secondary, for some missions a concealed PDW might be enough.
Otherwise it depends heavily on the ops environment, but blending in would be important, like:
For rural areas AK47/103 (optionally with UGLs), one or two marksman rifles like a M110, a PKM, some MGL, maybe a Javelin, hand grenades, plus some night-vision equipment. Basically no different than light inf.
For urban areas low profile is even more important -- silenced SMGs, low caliber LAWs, maybe some unusual and expensive high-tech toys like guided LAWs and unmanned sensors, &c.