RE: .223 vs. .22-250
Any reputable gunsmith can adjust these triggers down to 3 or 3.5 lbs. Also, if you plan to reload, don't try to push the pressures/velocities at all with the break action guns you pictured. They perform best with slightly reduced loads in most cases. For an inexpensive varmint rifle, you might look at the new Stevens 200. They have on sale around here for a little over $300 with a scope mounted.