So there’s a lot to consider here, but first consider there’s a reasonably decent little DAC (chip) and Amp (chip) built into your iPad.

Most headphones dongles are going to offer a better DAC and Amp built into one small unit. If you want a desktop setup, that’s when you get a DAC and Amp as separate units. To this point, search your local used market for an JDS Labs Atom Stack. They are a great value if you can get one. (Stack means both units, DAC and amp)

The sound of the 600s will change slightly but it may not matter to you when you consider the cost.

A DAC upgrade will improve the sound, but an amp more notably. The resistance of the 600 varies by frequency, so adding more power ensure the FR response is as designed. It may sound ever slightly more bassy or full on an amp. The main thing I notice with an amp is improved transient response, kicks, tings, bells etc. The initial impact is deeper and more punchy. This is because there’s literally more power available and this drives the diaphragm faster.