To make the scales more friendly to newer musicians, you typically want to frame a scale in such a way that it seems to have the notes modified as little as possible. To contrast the Eb and D# natural minor scales:
1 Eb D#
2 F E# -> (F) (we usually consider E# as F)
3 Gb F#
4 Ab G#
5 Bb A#
6 C B# -> (C) (we usually consider B# as C)
7 D C## -> (D) (we usually consider C## as D)
8 Eb D#
As you can see, more work must be done to translate the D# minor scale to the actual note, with a double sharp (in the melodic minor), meaning the note shown on the scale is C, but the musician must modify it with two sharps, and the actual note played is D.
In general, it is preferred to use the Eb minor representation for the above reason. However, if you change keys in the piece, perhaps to a more accessible sharp key, it would be reasonable to avoid switching from flats to sharps, and to stick with the D# minor representation.
If you don't have a particular piece in mind, start learning the Eb. But then work your way through all of the keys so that you can more easily handle more difficult pieces when presented with them.