For me, the answer would be easy because I really like Encores! I would go with the Encore. There are so many stock options, etc. available for it and Thompson/Center as treated me VERY well on items I sent to them for repair. In a couple of instances, I bought used barrels on eBay that malfunctioned and they repaired and shipped them back to me at no charge even though I told them I bought the barrel used.
As far as the caliber is concerned, from the 3 choices you gave, I would go with the 7mm/08 since it would do fine for varmints and deer and is a relatively low recoil inherently accurate cartridge. The other two would work as well though many would consider the .204 a bit light for deer. The .280 is fine as well but you probably don't need that much horsepower for varmints.
With the Encore, there are other very fine choices for the kind of hunting you intend to do. The ones that come to mind are the .22/250 Rem., .243 Win. and .25/06. Best of all, when you decide to go Elephant hunting, you can get a .375 H&H Magnum or a .416 Rigby barrel for it.