Jefflee1, I guess the first question is: why are you looking specifically at the 6.5mm. range of calibers? You mentioned "varmints and deer" as likely targets. While the deer are certainly suitable targets for this caliber round, varmints are usually shot with something rather lighter.
If you want to keep the varmint-and-deer combo in mind, I'd suggest dropping down to a .243, as this is usually considered a good round for both - bigger than the .224-caliber cartridges, and therefore suitable for smaller deer, but still small enough to use on varmints with lighter bullets. If you move up to the 6.5mm. range, you're getting more into deer territory, but moving out of typical varmint territory.
Also, there's a question of range. You're in Connecticut. I imagine that means that most of your shooting will be at short to medium range - probably not much over 100 yards for most shots. The .25-'06 is capable of reaching out to 400 or 500 yards with no trouble - wouldn't it be "overkill" for a short-range situation? Also, rifles chambered in this caliber typically have longer, heavier barrels (I've seen several with 26" bull barrels). Is this suitable for general use in wooded country like yours? In such terrain, I'd usually prefer a shorter, handier carbine type of weapon.
I'd like to suggest that you consider splitting your weapon use into categories. For deer hunting, why not look for a .30-30 lever-action carbine that can be cut down and fitted to your son? It'll do fine on CT deer over typical ranges, and won't cost very much. You could then look for something in the .224-caliber range for varmint use, or even go to a .17 rimfire round, for use on small varmints at typical CT ranges.
Just a thought...