Unfortunately the kit lens is poor.

• Sigma 16mm f1.4 DC DN is sharp but narrow.
• Samyang 12mm f2.0 AF is wider but has CA. Ill help you find others tho.

To add to the point above: be careful with that $400 limit since decent ultra-wides are pricey. I would suggest these two:

• Sony E 11mm f/1.8: Best choice imo. Its tiny and wide enough, but might push your budget.
• Sony E 10-18mm f/4 OSS: Try finding this used. The stabilization is great, tho be careful in low light since its only f/4. Make sure to check your crop settings too.

> Unfortunately the kit lens is poor. Yeah, I totally agree with that. When I first started vlogging with my camera, I tried to make the standard kit lens work for a trip to the coast. I ended up with so much footage of just my nose and forehead... it was pretty embarrassing to watch back later. After that, I picked up a much wider prime lens that I've been incredibly satisfied with. It really changed the game for me because I didn't have to walk around with my arm fully locked out anymore. The jump from a standard focal length to something like an 11mm or 10mm makes a huge technical difference on these crop sensors. Honestly, having that extra breathing room in the frame saved my vacation videos. My current gear has given me zero complaints, it just works perfectly every time I hit record. You'll definitely be happy once you get away from that kit lens.