First Time Bicyclist as a Commute Vehicle, need advice on good spring-fall bike.

Hello! This is a frequent question asked but I’m hoping I can provide more information through a post to help. Basically, I have a 20 minute commute (40 min. total) to work on a relatively flat urban street that I’d like to start using to bike to work instead of drive.

I have about $600 in my budget for a bike that I’d like to use for spring-fall, and then take the bus in the winter (I'm up north so extreme cold, snow, and pretty hot summers). I also plan on storing my bike in my apartment on a hook. What brands in this price range would you recommend, or what information do I need to provide to improve my search? I am also open to adjusting the budget a little bit if I can get a “forever” bike and only focus on maintenance.

Also, any good helmet recommendations too, as I’d like to not break my skull at a minimum. Thanks!

EDIT: I'm adding some bikes I've been finding, and will post them here. Some are below the budget by quite a bit, but the hope is to maybe get them tuned up/upgraded or use the leftover to get accessories. More info: I'm 6'0" exactly with about 31.5-32" inseam. 75" span so my arms are only marginally larger than my whole body. I'd like the bike to also be used for some grocery shopping some times, so I'd need saddlebags that could work for that, as well as any good bike locks and hidden spots for an airtag.

Ozark Trail 700c G.1 Explorer Gravel Bike $258

Retrospec Beaumont City Bike – 7 Speed $380