The valves can be checked with a simple compression gage. If they can hold pressure, they’re good. If not, they’re bad.
If they’re good, you need only do the timing belt and it’s accessories…the tensioner and the water pump.
Damage to the pistons can only be checked with the head off. If the head needs to be pulled, than the belt needs changing…and the tensioner needs testing, and the waterpump shoudl be changed, and on and on. Expect a big bill.
BUT…my impression is that the valves have already been determined to be bent. If you take the car elsewhere, you’ll need to pay for the first shop’s time & labor. Plug the tow. Find out how much that would cost. Tell them that the cost may force you to take it elsewhere and perhaps thay’ll negotiate or suggest and alternative. The final total cost may help your decision.
Oh, and unless there’s damage to the pistons from the valves hitting them, Id’ avoid replacing the whole engine. The replacement just may need a belt too and you’ll have no idea what problems you might be putting in.