The a6400 is a solid choice but the battery life is honestly pretty bad. Since you are on a tight budget, I would suggest focusing on power and comfort first.

• Make sure to get a Wasabi Power Battery 2-Pack and Dual USB Charger for Sony NP-FW50. It is much cheaper than the official ones and you will definitely need those extras for a full day of sightseeing.
• Be careful with that neck strap it came with. It tends to chafe after a few hours. I recommend the Peak Design Leash Camera Strap because it is easy to adjust and wont bulk up your bag.
• You absolutely need a reliable card so you dont lose photos. Look into the SanDisk 128GB Extreme PRO SDXC UHS-I Card which is fast enough for that camera. Basically, skip the filters for now. They mostly just protect the glass, and cheap ones usually make your photos look blurry anyway... just keep your lens cap on when you arent shooting.

Building on the earlier suggestion, I unfortunately had issues with sensor dust mid-trip that ruined every single shot. Get Giottos Rocket Air Blaster Medium cuz cleaning kits are way more stressful...

@Reply #2 - good point! I would suggest the SanDisk Extreme PRO 128GB SDXC UHS-I V30 to prevent buffer lag. Check the Camera Memory Speed site for benchmarks so you dont buy slow cards.

Saw your post earlier and honestly its just ridiculous how much pressure they put on us. You are right to be stressed because the whole system feels like a trap lately.

• It is such a scam that these brands sell you a high end camera for thousands but then expect you to drop your last cent just for the basics to make it functional.
• The fact that you have to worry about your gear being a paperweight because of one forgotten tiny plastic bit is honestly insulting.
• Companies just dont care about the user experience anymore, they just want to milk every penny for extras that should have been included from day one. Its honestly enough to make you want to leave the camera at home and just use a phone, which is sad cuz you worked so hard for it. The gear anxiety is totally real and the manufacturers are 100% to blame for making it this complicated for people who just want to take nice photos on vacation...

Building on the earlier suggestion, you really dont need to drop a ton of cash to have a good trip. I remember my first big solo trip where I had basically zero budget left after buying the body. Making it work with stuff I already had around the house was the only way.

• A thick wool hiking sock worked as a lens pouch inside my normal backpack. It saved me from buying a dedicated bag.
• Instead of a fancy padded strap, I took some adhesive moleskin and stuck it to the underside of the stock strap. It looked a bit janky but it stopped the chafing during 10-mile walking days.
• Cleaning was just a microfiber cloth I got from my eye doctor. The DIY route works if you are careful. Honestly, the biggest lesson I learned was that gear is secondary to just being ready to shoot. Three weeks without all the bells and whistles went fine and the photos were great.

I have been shooting with Sony for years and honestly, I am going to politely disagree with the push to buy a bunch of extra gear. You can probably get by with the stock accessories and keep your $100 for your actual travel expenses.

• Power: I think the a6400 allows for internal charging via USB. If you already have a portable power bank for your phone, you might not even need to buy extra batteries. IIRC you can just top it off during lunch or on a train.
• The Strap: The stock Sony strap is actually very strong. It is not the most comfortable thing for a 12-hour day, but it is functional and safe. You wont lose your camera using it.
• Filters: I really do not think these are necessary for a beginner. Someone told me they can actually lower your image quality if you buy the cheap ones, so it is probably better to just use the lens hood for protection. I am not 100% sure about your specific shooting style, but the basics in the box are usually enough to keep the camera from being functional. It is a solid system on its own.