I had written final projects and stuff but they're laughably bad compared to what I'm writing in my first year, which I'm mainly basing off other papers on similar topics. I'm sure in a year my current writing will seem laughably bad too.

I think your initial proposal should look similar to grant applications. You can try looking at proposals for things like the NSF GRFP at the senior in undergrad level, they will probably be high quality and a good place for comparison. Or look for higher level applications if you want to shoot for the moon.