They just about summed it up. Personally I wouldn't worry about Beta until later on in Disc 1 at the earliest, as you definitely don't need it, it's just not worth the time you lose hoping to get the right situation with Midgarzolom to get it. But definitely go for Matra Magic, Flame Thrower, and Trine early on. I think you can also get Frog Song early on, from frogs either in the forest between Gongonga and Cosmo Canyon or in the Temple of the Ancients (I definitely know it's there). You might also wanna grab White Wind from the big owl dudes around the Junon area once you get the Manipulate materia.

As for me, I like to give Enemy Skill to Barrett - why shouldn't his GUNARM be a multi-purpose weapons system? Matra Magic and Flamethrower both make sense to me on there, although some of the more "magey" spells don't quite... But it makes sense for a while! Also, Barrett's magic stats are some of the weakest in the game, so it's good to give him some abilities (and something to spend MP on) that aren't necessarily tied to stats.