With Horizons came the ability to "synthesize" temporary improvements and replacements to your ship, like ammo for the guns and refills for the AMFU repair units. One thing an explorer can synthesize that is actually useful is a one-shot jump range boost (it's usually called "jumponium" here on the forums). If you left the Bubble pre-Horizons, then you won't have an SRV on board, so that won't be much help to you out there now. With Engineers came the ability to mine rings and asteroids for the elements needed for jumponium, but unless you happen to have brought a mining laser with you, this too will be useless to you. But, since you're travelling corewards, jump range boosting is a luxury, not a necessity.
Black holes, white dwarfs and neutron stars are deadlier than they used to be. Black holes now heat up your ship if you get too close (rather than simply let you fly right through them) and NS and WD stars now have "jets" spewing out of their poles, which send you spinning out of control if you fly into them carelessly. Flying into them carefully can give you a "supercharge", not unlike jumponium, for a one-shot jump range boost, but be careful: dropping out of supercruise while inside a jet is an almost guaranteed death sentence. Supercharging also does 2% damage to your frame shift drive, so don't do it if you don't have an AMFU or two, unless it's an emergency.
The good news is, it's not quite so lonely out there any more. A "second bubble" of a dozen or so human colonies has been founded in the Colonia region, situated about 4/5ths of the way to the Core but off to one side (so if you were straight-lining it to the Core, it's probably still a couple thousand LYs away). Jaques Station in the Colonia system has everything you need for restocking, repairing and re-equipping your ship, as well as a convenient safe harbour for selling off your data. There are also half a dozen waystations founded on the route to Colonia, but you do need to own Horizons to land on them as they're all planetary bases.
The recently introduced Passenger missions won't change what you're doing out here, though you might stumble upon a Tourist Beacon, especially at Sag A itself and in the Colonia region. If you see an oddly-named navigational point as you fly around a system, it's probably a tourist beacon. Tourist beacons are put there for Passenger missions, but you can still stop and scan them without passengers on board, if you like. Most of them tell you a little story about the place the beacon is situated at.
Unknown Aliens. They're pulling people over in the Pleiades region and scanning them. We simply don't know if it's possible to encounter them anywhere else in the Galaxy, but unless I'm old news, they haven't been reported anywhere except around the Pleiades. So far, all they do is interdict you out of interstellar hyperspace, temporarily disable your ship, scan you, then leave.
