Forget a 2.0 elite, no such animal. The Omega started off as a 2.0 8Valve, select spec, the moved up to GLS spec, and then headed upwards in refinements.They were designed as crusin' machines to wisk company directors around the country in style and speed, eating up motorway miles. You chuck it into a corner, it weighs 2 tonnes, it will not behave like a skoda
School run/Omega Elite eh... not really the the intended use. Maybe not the ideal car ?.
My 2.2 Omega was fine at acceleration, not mega fast but fine, no problem overtaking buses !.
Most generations of Omega's have plenty toys, the early GLS may be not but most early Elites, Prefacelifts and Facelifts have plenty toys.
Auto's have their place, my morning commute is the M62, and its so easy, one pedal for stop, one for go, cruise, power steering, its there.

Saloon are nice, however the estate's have a cavernous boot, I have heard of 3 piece suites going in. It all depends on your needs.
Petrol is a problem, it depends on your right foot

however one plan of action is to get it LPG'd asap. That halves your fuel costs. OK you loose a bit of boot space but fuel at 67.0p/L
So to summarise, most of the Omega's out there are excellent choices, lots of bargains. My 03 2.6CDX was £750, and the engineering is a class above other makes with their stick on LEDs etc. On here we know most of the problems, things to be serviced regularly, and there is a thriving community of people breaking cars so spares are easily obtainable.
Ken