First, double your budget.
A lot of people will recommend used bikes---those are people who are completely out of touch with what it is like to know nothing about bikes. Unless you have a good friend who knows a lot about bikes I would buy new bikes---nothing like getting all excited to go ride your "new" used bike and find that it needs a couple hundred in repairs.
Honestly ... go to Walmart and buy a couple Mongoose Hotshots---about $100 a piece, not really strong but not terrible. (
https://www.walmart.com/ip/700C-Mong...ange/143302742) Take them to a local bike shop for a check-up/tune-up and to make friends .... if you find a shop with friendly, helpful staff, tell them that you plan to buy better bikes in a season or two ... tell your story. They will hopefully treat you right in hopes of getting future business. If the staff gives you Any kind of attitude about your Walmart bikes, walk away.
The reason I suggest those bikes is because your expectations are unrealistic and your continued participation is uncertain. You really aren't going to find a worthwhile bike---the kind you would keep for five or ten years of regular use---for less than about $600. So instead of spending $600, you would be looking at more like $1500 once you add helmets, water bottles and cages, maybe lights (safety during the day, Survival at night,) seat bags, tools tubes, patch kits, pumps, maybe a rack for the back of the car ... all the little stuff adds up.
If you Knew you were going to ride a few times a week around the neighborhood and most weekends, then the investment would make sense. If there is a 30% chance that you will not be riding a year from now .....
So ... either double your projected investment (at least) or consider getting some very simple, very cheap bikes for the rest of the summer. if by the middle of next summer you find that you need better bikes, you will have a Much better idea about what to buy.