All three rifles you mentioned would be great shooters, but I would give the AK my vote. Mini's are great, but factory (reliable) mags are uncommon and pricey. The second generation of the Sig 556R's are awesome, but your a little more limited to what mags it will use (US Palm and ((10)) Waffles are a no go) and you'll need to buy optics / sights. The AK is tried and true, as well as in service with soldiers around the globe. Arsenal would be the route I would go, in a Bulgarian SLR. The Izhmash SGL-21's are nice, but are actually AK-74's chambered in 7.62X39 thus making many surplus parts incompatible. VEPR's are built extremely well, but take a lot of work to turn into an evil black rifle since they are imported in a "sporter" configuration. The AR's chambered in 7.62X39 have been attempted by several of the big gun companies(RRA, Colt, etc...), but almost always suffer from reliability issues plus mags are uncommon.
Good post though I would lean more towards the 556R, but just by a little.