I can tell you that in California, the speeding ticket would not be a problem. The DUI would result in a 6-12 month administrative drivers license suspension. The suspension can be challenged if you request a hearing (or an attorney does for you) within 10 days.
These suspensions should always be challenged, because if you win the hearing, you get to keep your drivers license even if you are convicted in court. Also, you get a temporary drivers license to allow driving until the hearing is held, which is sometimes months down the road.
You can apply for a restricted drivers license to get to work and school during this period.
A DUI arrest also results in 2 "negligent driver points" on your DMV driver history repost.
If you are convicted, the DMV will also require you to install an alcohol detecting ignition interlock device on any car you drive or own.
A DUI conviction will remain on your DMV record for 10 years.
Many other states follow the same pattern, but some are different.
I'm licensed in CA only. Report for your state if necessary.
Hope this helps.
Questions? I've handled more than 100 DUIs with DMV problems. I know the process very well.
If you want a phone call, let me know. I am available.