The Friday start is the most common timing here for that reason - day 3 on a weekend gives you room to rest if needed. Some people feel nothing, some feel rough through day 2 or 3. Either way, noting the actual injection day is useful so you can track how each dose week goes.
RE injecting near the site:
I doubt it matters for a GLP like Reta. It's not like a localized healing thing. But could be worth a try. I'd stick to the belly fat though.
I think Monday mornings at 5:30 AM when I wake up will work best for me. Gives it time to kick in, I can hit the gym, and then chill during the day. I'm a really light sleeper, so anything to keep my heart rate down is a win!
I'd suggest pinning in the AM for your first go. Wouldn't wanna inject at night, have a bad reaction, and screw up your sleep. Also, maybe do it on a weekend when you're off work. Just in case you have some weird side effect that makes working tough. After the initial pin, the timing prob...
It's amazing how some people get weird when you start losing weight, especially with a little injectable help. Some folks just try to bring everyone else down. I noticed who got uncomfortable as I slimmed down too.