Great camera! Quality image, front-facing screen, and it's light, it's like it was made for vloggers.
Gimbals for vlogging are going to be motorized. 3-axis to minimize motion in every direction since it's handheld. But it gets expensive. And it needs to be powered. So you can go with a purely mechanical solution like a steadicam. The downside to that is the extra bulk for the counterweight.
So look up the DJI Ronin-S, Zhiyun Crane, those are the better gimbals. For steadicam you can build your own or look up Loha and Imorden's offerings. Another option is the Joby Gorillapod Focus. The bonus to that is you can wrap it around a lot of things for creative positioning. I've been using their stuff for years for photography and now for videography. Note that you need to get the Ballhead-X as well to mount your camera.
For mics look up the Rode Videomic Pro and Shure Lenshopper series. They're both shock-mounted to reduce motion noise, and they're shotguns made to reject side sound. They're intended for this application, so you can route it directly to the camera to keep the rig light. Been using both brands for a long time, can't go wrong with either, so if you can demo them it's the sound characteristics you're after.
You'll want spare batteries for anything that is powered. If you are going where it is very cold, keep in mind batteries underperform. If it's VERY cold (below freezing), you will want a handwarmer and an insulated pouch (or use a pocket) to stick the battery near it to rejuvenate it. If using a chemical handwarmer, make sure you can revive it (it needs hot water, you can stop up a sink and use a coffee maker to boil water), but they make air-activated disposable ones too.
You'll want multiple memory cards, and are you bringing a laptop? You'll want to offload the cards at day's end (cards are more prone to data loss than a hard drive). I don't bring a laptop when I travel light. What I do is attach a USB hub to my phone (it's OTG capable), then attach a card reader and portable hard drive to it. I use a file manager on the phone (ES Explorer Pro) to copy it from the card to the hard drive. My phone provides enough power to run this, since the hard drive is an SSD mounted in a case. If you're using a mechanical hard drive, the USB hub probably needs to be powered.
You'll want a case for the memory cards. I like ThinkTank's Pixel Pocket series since it's compact, protective, durable, and it can attach to your belt, bag, whatever. You'll want a bag to carry all this stuff. I like Peak Design's sling (was offered on Massdrop) when I travel light. Straps on the bottom could hold the gimbal. Backpacks are an option too, since you probably want to carry other stuff. Look up ThinkTank's options, I've been using their stuff for years for photography, and they've got a solution for everything.
You could use a compact 18% grey card so you can color balance it later, or just color grade it freestyle. If using a grey card, just hold it up with your free hand when you start filming yourself. If you change position (since the lighting changes), hold it up again.
You also want a compact/mini LED light box if you think you'll be going some place without a lot of light or at night. To save space you might not want the bulk of a box but this you'll have a harsher light. Or you could just tape paper over it to diffuse it a bit. Then there are ring lights to make you look sexy that go around the lens.
Oh yeah, lens. Not familiar with the Lumix's options but like I said, a 50mm equivalent for up-close journo-style. Consider a wide zoom if you want to capture the scenery around you. 10mm-24mm equivalent, something around that range, nice and flexible. Note focal distance, make sure you'll be in focus at arm's length.