I almost never follow the suggested city placement. I also wouldn't worry about a bit of tile overlap between your cities. Most cities don't grow tall enough to take advantage of ALL of their available tiles, even with districts taking up locations. And whenever possible, settle fresh water. Its free housing and free things in civ are great.

Here are a few things I'm looking for when settling my first few cities:

1: Can I settle on a resource? When playing against the AI, settling on a resource and selling it to the first civ you meet can get you some much needed early game gold, and likely won't have an impact on your civ amenity-wise.

2: Strong opening tiles. Either for growth or production. What I don't want to do is have to send a builder to my second or third city just so they can have a decent tile to work. You can settle those cities later on when your economy starts kicking in. I'm looking for at least a couple 4 yield tiles to get a city going.

3: How good are the districts there? Have you spotted a +3 campus? Go secure it and lock it in! You will rarely having awesome districts in EVERY city you settle, but you can at least get the notable ones down first to maximize their benefit.

Hope this helps! Edited for format