Hi!
Almost all of MD's laws regulate point of sale, not posession/ownership.
You do not have to register any (non-NFA-regulated) rifles, pistols, or shotguns on moving to MD. There are some "Assault Pistols" which are flat-out illegal, but they are listed by name in the law.
You may own/possess magazines holding more than 20 rounds, but you may not sell them, buy any, offer to sell or buy any, loan, lend, lease, rent, etc.,etc. them. Most residents go to PA or VA to buy "standard capacity" mags if they want them. That does seem to be a(nother) loophole.
A DUI is trickier for me to answer. I recall having "have you received a DUI/DWI ..." on the list of questions you're supposed to answer "NO" to on the form, but it has been a while and now I can't recall the specific language.
That would be a good question to call a few gun shops with. I'd say ask the MDSP firearms division, but they are not very helpful people. Hate to say that, but they really couldn't be bothered and have always acted VERY suspicious when I've called with a simple question. At the least, a dealer (or three) could read the form and tell you what it says.
If you can avoid MD, by all means do so. Maryland sucks.
Good luck!