Ordering from Amazon US is no problem and very reliable. They sometimes use DHL but more and more they use "AMZMX" which presumably is their own shipping service using local contractors. I have found both to be reliable, although AMZMX is less trackable.
I find that if the same product is available from Amazon US and Amazon Mexico, it's usually a little cheaper to order from Amazon US, including paying the shipping and "estimated" duty. I have actually had refunds of a few cents when the duty was below the estimate paid.
As Joco said, if you set your default shipping address to a Mexican address, you will be informed whether a product will ship to Mexico as soon as you view it. Most things that are shipped by Amazon will ship here, but items shipped by third parties may not.