In my experience, you're totally right to be cautious about that internal audio—the ZV-E10 II is a beast for video, but that built-in capsule just cant handle a stiff breeze lol. If ur choosing between those 2, here is the technical breakdown. The Sony ECM-G1 is super reliable cuz it draws power directly from the MI shoe. No batteries to fail and no cables to snag, which is a huge plus for reliability. BUT, if wind is your main enemy, the tiny deadcat on the G1 is... well, it's just okay. For a solo creator, I highkey suggest looking at the Sony ECM-B10 Digital Shotgun Microphone instead. It usually stays under your $250 budget and actually utilizes the digital audio interface in the shoe for a cleaner signal. It has three pickup patterns and way better noise suppression tech than the G1. If you go with the Rode Wireless ME, it's great for flexibility, but you gotta manage 2 extra batteries and that messy 3.5mm cable hanging off the side. Honestly, I'm satisfied staying within the Sony ecosystem for the Mark II... basically keeps things simple so you dont miss the shot. gl!

+1 to what was said earlier! Honestly, MI shoe mics are literally a lifesaver for solo creators. Since you have a $250 budget, here are two killer options that handle wind way better than the G1: - Sony ECM-B10 - It’s basically a beefed-up G1. The digital processing is amazing for blocking background noise and wind, plus it's still cable-free.
- Deity V-Mic D4 - Super budget-friendly and comes with a great deadcat for those breezy vlogs. Both are super easy to manage, right?

Honestly, i feel your pain so much. I've been dealing with the same thing on my ZV-E10 II and it's basically the most frustrating part of the whole setup. It's just so unreliable when you're out in the real world. You think you've got a great setup, but then a tiny breeze or a loose cable ruins everything. The internal mic is basically useless outdoors, and even some of these external ones feel like they're gonna snap off or lose connection if you move too fast. The whole reason people look at stuff like the Sony ECM-M1 Digital Shotgun Microphone is to avoid that nightmare with the 3.5mm jacks. Using the MI shoe is more about reliability than anything else, cuz those cables are just a disaster waiting to happen. But even then, the wind noise is such a constant battle. It really kills the vibe when you're trying to be creative but you're just constantly paranoid that your audio is gonna be trash when you get home to edit... it's honestly exhausting.

sooo, for your situation, i would suggest staying with the Sony brand for that camera. honestly, their MI shoe-powered mics are basically a game changer for vlogging! - stays super compact
- no messy cables i'm pretty sure you'll find the native gear is just more reliable for solo shoots. but be careful... make sure to use a high-quality deadcat! peace.

Building on the earlier suggestion about sticking to the Sony brand for that MI shoe connection, I actually have to disagree a bit on the shotgun mic being the best fix for wind. I have been super satisfied using the Sony ECM-W3 Wireless Microphone lately and it works well for exactly what you're describing. While shotguns are simple, they really struggle when you're moving around or if the wind is hitting the camera from the side. With this wireless set, you get that same cable-less MI shoe reliability that makes the ZV-E10 II so easy to use, but the mic stays right on your shirt near your mouth. I dont have to worry about a 3.5mm cable snapping or getting loose in the jack, which is always a huge concern for me when I'm out vlogging alone. Its honestly such a relief not having to triple-check your connections every five minutes... plus the deadcats that come with it are actually legit for outdoor shoots. If you want something that just works and keeps your voice clear no matter how breezy it gets, this is a much safer bet than a standard shotgun mic imo. It fits your budget perfectly and keeps the whole rig feeling very professional and tidy.