Her instincts are a little a mess here - there's so many new sparkly things to deal with! But in terms of prioritization...
Magic things, big downside risks from supervillains, figuring out something for immortality, and helping the green lantern corps out are all reasonable places to start, and seem at least kind of tractable? Magic research probably is something that she'll need to get a bunch of consultations around before she can really get much of a sense of what's reasonable to do without being directly babied by her power or just going into the research cave and plopping in a bunch of powers around various subfields and writing herself primers on what's what. Call that plan B.
She pokes around online a little - back home, there's the FBI and Interpol most wanted lists for the most notable criminals still at large - is there something like that here? The league does seem kind of criminally undersupplied with trackers, in her opinion, and she should be able to change that with a bit of work.
Oh and... speaking of supervillains... Sinestro has a ring like the green lanterns, but with a different color that looks to work a little differently? If there's two, there's probably more. Can she get a power that tells her something about the different colors and what they do? Honestly, a power for that isn't likely strictly necessary, at least for identifying the colors, since she can just poke the Gift with a big list of colors and/or emotion words to try to figure what colors have what emotion and then try to get it to pitch powers unique to each color? Yeah, that sounds like a reasonable idea, let's!
Themiscyra is weird! An island of immortal women patroned by the Hellenic gods is not exactly within her experience. There's got to be something that she can do with that - it's not like there are no people who are already faithful off paradise island, and a lot of people convert. Really, it depends a lot on the leadership situation and what the magic there actually requires. She goes and tries to book a time with wonder woman - if nothing else, she does want to talk to someone about her options for weapons and combat training, and hopefully she'll be able to enlighten her a little about the situation, there? Being polite and taking it at least a little slow is probably better than trying to rush it as dramatically as she really wants to.
As for her powers...
She does really kind of want to break down and reoptimize the green light stuff - the aura half of the 4 pter is pretty tangentially related. The basic core of the imbuement skill power, the willpower power, and the deepening power is good, and adding an associated skill is probably a good way to make use of a 3 pter slot. As for what she can do with the rest of the points, if she's doing a dedicated build...
Something around 'lanterns', whatever those are? More skills - she really does want to pick up some sort of mobility option soon... She's not touching magical bond powers until she can get some oversight there. Probably the guardians have figured out most of what there is to figure out about the purely green light side, but she wouldn't be surprised if she could upgrade them meaningfully in a different direction. Does the will-shroud effect linger on the items she imbues? If it does, that's an angle all on it's own to try to upgrade the entire corps. It's probably not a huge edge, but if it's an indefinite buff to control and makes it easier to use inconspicuously at important moments... That could be huge, even before considering other things she could add.
Decisions, decisions.