My general rule is to live there for a year so you can see what's there. Some of those "weeds" might be plants you would want. Stream fed ponds are my dream. So much better than pumps and filters. Go slow and enjoy the process.

Can you dig out some at both ends of the "land in the middle" and make the pond bigger with an island and an arched bridge to go to the island? Trees and shrubs around the pond would make it look more natural.

Maybe it is the swimming pool technician in me...but that looks like an 80% finished lazy river. Don't make up your mind right now - just think about it.

My first thought was something like this link (not mine, found in a google search)
Long rectangular lily ponds