As a first attempt, I'm starting with the assumption that the notation
system I'm looking for will have names for 4/3 and 3/2 -- for simplicity
I'll call the 1/1 "D" so that I can use "G" for 4/3, "A" for 3/2.
Pitches near these notes will use accidentals. 7/5 can be notated G +
21/20 or A - 15/14, so it won't be necessary to include it in the basic
scale unless the scale has enough notes that the gap between 4/3 and 3/2
is too large.

So, with a list of intervals likely to be used in 7-limit scales, I can
identify 81/80, 64/63, 36/35, 28/27, 25/24, 21/20, 135/128, 16/15, and
15/14 as some of the more important accidentals that will be needed. The
importance of superparticular ratios is one of the ideas that I've
established for Zireen music, so I'll want to take another look at that
135/128.

21/20 * 225/224 = 135/128

Since the difference is relatively small, the 225/224 could be
represented as an extra mark (e.g. a hook or a slash) added to the main
21/20 accidental. Note that the pairs (28/27 25/24) and (16/15 15/14)
are also separated by 225/224.

Note that 50/49 and 49/48 are not included in the list of accidentals.
Since these are so close together (2401/2400 apart), it would be
convenient not to need both of them. The easiest way to do this would be
to use a temperament that tempers out 2401/2400.

49/48 is the difference between 8/7 and 7/6. 50/49 seems to be mainly
needed for ratios containing 49 (e.g. 49/40 * 50/49 = 5/4).

Not counting 49/48, you've got 5 basic size classes of accidentals.

81/80, 64/63
36/35
28/27, 25/24
21/20, 135/128
16/15, 15/14

This suggests something around 53-ET as a first approximation. 53-ET has
some useful properties, but tempering out 2401/2400 isn't one of them.
Another approach is back to 171-ET, which does temper out 2401/2400 and
has a step size near 225/224.