Each point in Strength (and by extension, Attack) makes a respectable difference, and four frames for an extra point of Strength seems pretty damn tiny. For example, 36 Attack at level 7 has a base damage of ~46, while 38 has ~49. You can triple that for Braver. Extra points in Strength and Magic (if it's used at all) could very well be important early on; Braver is barely able to kill Dark Nation as-is, for example. It's entirely possible to keep stats at their upper limit:
Now that the Baseline for the next Level has been found, we must still work
out how much the current Stat may rise. This is worked out by first
calculating the following value:
Stat Difference = Rnd(1..8) + Baseline - Current Stat
This difference is then capped at 0 to 11 inclusive, and then the following
table is used to look up the final stat gain:
Difference Stat Gain
0- 3 0
4- 6 1
7- 9 2
10-11 3
From this, we can see that you can only go a maximum of 5 points over the
Baseline before you cannot gain any more points, and if you are more than 8
points under the Baseline, you will automatically get the full 3 point gain.
Over the course of 98 levels, this makes sure that you never stray too far
from your intended average stat.
This also means that stats do not need to be manipulated after every battle if they need to be at a certain level later, as 2 or 3 level gains will most likely be enough to raise them back up.
The only other stats I can think of as being useful to raise are HP, Luck (for faster crit manipulation) and maybe Dexterity, as some of the early fights (Motor Ball, Jenova*Birth) get pretty long, and this might allow for an extra turn somewhere.
In other tactics, all I can think of is that maybe Lunatic High would be useful somewhere, but by the time Red would get it there aren't really many long fights left.