Help a newly level 99 Smn gear up,setting goalsFollow

Abyssea is where you'll be doing most of your catch-up. This is a good place to start reading:
http://wiki.ffxiclopedia.org/wiki/Abyssea

I'd start by focusing on some key items rather than actual equipment. Try to learn Abyssea, unlock each zone, unlock each conflux within each zone, get a couple abyssites of merit, a couple lunar abyssites, and a couple good atmas. Once you have those things, you can start looking at farming some equipment from Abyssea, your main goal being the Caller's empyrean armor set. A full set of 5/5 Caller's +2, as well as Caller's Pendant, are the keystone of any good Summoner's equipment these days.

Until you get better equipment, one that will help a lot is Minikin Monstrosity. It gives 10 mp/tick refresh, among other things. It drops from Durinn, which people will sometimes farm for AF3+2 items. So you might have luck finding a group that way.

Ultimately, the ones you'll want to have are:

For physical damage: Razed Ruins, Voracious Violet, Gnarled Horn
For magical damage: Ultimate, Beyond, Minikin Monstrosity
For solo: Ducal Guard, maybe Mounted Champion

Note that Ducal Guard is a quested atma, it requires fame which isn't too terrible to obtain. Ducal Guard makes your avatar damn near invincible. Also, Ultimate is a synthetic atma, meaning that all you need is a certain title in order to purchase it for cruor. In the case of Ultimate, you need to kill Proto-Ultima in Limbus. Once you do that, the option to buy Atma of the Ultimate will be available. All the other atmas I listed are obtained from killing stuff in Abyssea, and often will only drop if you trigger red weakness.