OK, first off take adeep breath and try to relax. It has been three years since your last ticket - right? You are going to have to go to your state NDR to find out how far back the record goes. 10 years used to be the "stadard" answer, but 9-11 changed that: now the FBI is involved so all kinds of strange things come up - it used to just be convictions within 10 years - but now it seems that ANY contact with law enforcement - EVER - is fair game. I'd be ready to talk about all of these tickets.
I could be wrong, but I think you're OK. What you want to avoid in your background check is any thing recent relevant or really really bad.
My advice to you:
- Relax - the old tickets are a done deal, don't try to hide them, but don't stress, you can't undo them now.
- Stop speeding! you have a trend going, you need to show that you are reformed.
- Consider taking a driver safety course. You can do this to lower your insurance rates and by doing it voluntarily you can show that you really are reformed and that you want to follow the law now.
Good luck!