The First Order

Ah I got it. No problem there then.

As for patrol crafts, I guess any TIE-model, equipped with a hyperdrive within the First Order should do. This would include the standart one as well as the TIE/sf, if you're looking for a starfighter, manned by two crew members. Those are pretty standart among the First Order and a solid choice for beginning pilots. Alternatively there also is the TIE Predator, which some fleets run as well.
If you're more interested in a bombing craft, we also have the TIE Demolisher as a standart bomber. Another alternative would be as well the Neutralizer-class bomber, as I would assume both have their pros and cons, though statwise the Demolisher is of course an improvement over the Neutralizer.
If Admiral Needa is to be believed, you might also want to trust in a TIE Defender. A more older model, but not necessarily a bad one as it is quite balanced.

For patrol crafts, which are capable of operating within First Order systems on their own, I can recommend one craft I designed as an FO replacement to the TIE/sk : The TIE Harbinger.
This starfighter is pretty much made for planetary defense as most of its utility gear is optimized to feature not solely a hyperdrive, but as well an astromech.
It's main drawback is a decrease in speed, therefore making it slower in terms of space travel than other TIEs, but given its role it should be utilized as either a special forces craft or a more defensive craft. Perfect for system patrols and dogfights against other vessels within its class, but maybe not the best choice for a craft which is supposed to pursue anything as fast as a regular TIE fighter.

On the contrary there also is the TIE Vector as a more aggressive model which pretty much gives the opposite of the Harbinger: More speed, more attack, less defense.
This one is pretty much build in the image of the TIE Interceptor (of which there will also be an FO version at some point since one does exist in canon) so that might be a choice as well.

The more advanced models following afterwards would be the TIE/vn and the TIE Phantom, as both of these starfighters actually possess cloaking devices. The TIE/vn furthermore features a hyperdrive, making it potentially even more harder to hunt down if it needs to escape. Those are limited among player characters, but also a possibility for flying one as a pilot. Yet that might be the late game for your own plans.

So yeah, rough overview in terms of starfighters. I could also look up support craft or recommend other patrol crafts if needed, but those would be my recommendations.

(and I also need to fix up the broken picture link on the Neutralizer :< )

Oh my bad!
Misread some stuff then, sorry!

As regarding patrolships both the Lancer-class frigates and the Gozanti Cruisers feature hangarspace, although the Lancer-class utilizes it for shuttle space.
The Gozanti is probably the best vessel of choice for smaller patrol jobs, as it can carry 4 TIEs at the same time.
While a category larger there also is the Quasar Fire-Class Bulk Cruiser, featuring normally 48 starfighters per ship - for patrols this ship is also ideal, given that most FO TIEs have a hyperdrive on board and thus allow it to function as a mobile base. Pretty much a flying hangar which can fly from imperial ports to another.

Other than that we tend to utilize quite often the Vindicator-class Heavy Cruisers when we're talking about larger ships, featuring around 72 starfighters within its hangarspace. Around the same size category we have also with less starfighters the Nebulon K-class frigate, which also carries 4 TIEs if you prefer serving on a larger patrolship with one individual flight.

Just suggestions of course in hopes that I can give you some good ideas of what you might like.

Seems like a solid squad. That or a Tartan-Class Patroll Cruiser, depending on how small/big we go can do the job. Or one of the Raider-Class Corvettes might suffice, as both of these are nice for patrols.

As regarding planets, the First Order has plenty. Before Coruscant Jenia's and Viggo's forces trained over New Carida, which is known for being the best system in terms of troop training, but planets with larger shipyards like Kuat or Rendili are also not unlikely for a cadet to start. Or around the former capital area of Muunilist and Mygeeto it might also be an option. Guess that depends on your personal preference though since patrols could be anywhere.

Sounds good, that means I need to figure out where Jenia Kasalle is taking Incursio.

So what world would be a good place to start Xoia. Looking for a world that smugglers and pirates would be looking to steal or hijack Imperial goods and resources, but something a little more off the beaten path and wouldn’t have serious defenses, especially, as I’d consider it for story purposes, much of the fleets are currently at Coruscant and they were the closest available team to intercept the thieves.

I feel that Rendili and Bastion would have serious defenses though, Harnan. One is a shipyard world and the other is a very important Imperial world. Khomm is likely the better choice of the three suggested.

Ilum or Khomm works.

Time to take down some crystal raiders then.

Well, I've got a fancy oversector and no ISB agent attached to me. Be glad to have you!