Hi Tom,
I would like to start with welcoming you to the Board.
Secondly, I will share with you what I did (with research thru our Board here) to clean my rusty Cast Iron Grates.
1) Use a wire bush and clean off all the rust that you can.
2) I followed that up with Loctite 'Naval Jelly Rust Remover' that I bought from Home depot. Followed the directions 100% as indicated on the label.
3) Just to be safe (I am very Anal), I than dipped them in a vinegar/water solution mix 60/40 ratio, and cleaned it with brillo pad.
4) after they air dried for about 2 hours, I sprayed it (light spray) with generic veg.oil, and baked them in the oven on a 250 F. for less than a n hour.
They were not perfect, but 85-90% was acceptable for me.
All I do now, is use peanut Oil after every 4-5 cooks (with brush) and brush them after the cook when the temp. of the grill has lower.
I am sure a lot of other members can & will share their success stories with you as well.
Once again, welcome.