I have some helpful hints...not the least of which is don't use apostrophes incorrectly
The big drawback to mounting on the carry handle is that the scope sits up very high over the bore, and eye relief will be a problem, depending on the length of your scope. Higher power variables will be in the neighborhood of 12" long (for starters), and much of that length will be aft of the adjustments...putting the eye of the scope out over the buttstock. Add another 3" or so for a standard amount of eye relief (how far back your eye needs to be from the lens to get the full field of view), and you'll end up with your face way back on the stock.
To get around that, look at shorter scopes, and stay away from scopes that need 4" or more of eye relief.
You won't have too much to choose from given your budget, but you can at least compare these factors as you shop.
Sightron makes a 3x9x40 mil dot scope that Midway has for $109. It is the best "cheap" scope I've ever bought....VERY clear glass, it's bright, and the clicks are very positive. It's a tad more than your $70, but I can tell you without a doubt that "made in Japan" scopes are better than "made in China" scopes, and in this case, I think the extra $40 will be well worth it. It wouldn't be my first choice for a carry handle mounted scope, though.
I'd concentrate on shorter, lower power variables in the 1.x-4/5 range. In your price range, several folks here have gotten the Simmons Pro Diamond shotgun scopes, and seemed pleased with them. They're around $60, aren't too long, and don't weigh too much. I have a Simmons 8 Point 1.5x5, and I've played around with it on the one A2 upper I have.
The old Colt 4x scopes would be perfect, since they are designed to to on the carry handle, but they're too much money. I've seen Hakko knock offs of these, but they're in the $170 price range.
BTW, there are cheaper mounts out there than the ARMS...not as good, but I figured I'd mention it.