I am trying to have a better idea on the importance of an external dac/amp.
Nearly everyone says that the M50's don't benefit from an amp. Typically cheaper headphones need amps less than more expensive headphones, so choosing between cheap headphone + amp or expensive headphone without amp probably isn't a good choice. An amp isn't going to magically make a headphone sound better; some headphones just have lower sensitivity or don't do well from outputs with certain characteristics, so using a certain type of amp with them will improve the sound quality.
I think the best route would be to get a more expensive pair of headphones that don't need an amp. I have never heard the DT1350's but I did own the M50's for a short while before returning them, and I would guess that the DT1350 is a better headphone than the M50, which frankly is a bit overpriced at $150. Also keep in mind the DT1350 is on ear while the M50 is around ear.
Also look at the Shure SRH 1840. It doesn't need an amp and has a less U shaped frequency response than the M50 (I found the treble on the M50 to be too harsh and the mids too recessed). However the treble on the 840's is a little biased towards the high end, so cymbals have more "tsss" and less bell tone when compared to other headphones. They also have a noticeable mid bass hump. You can get them for under $200.